id	sid	tid	token	lemma	pos
ma-136	1	1	2023	2023	NUM
ma-136	1	2	ada	ada	PROPN
ma-136	1	3	academica	academica	PROPN
ma-136	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-136	1	5	.	.	PUNCT
ma-136	2	1	j.	j.	PROPN
ma-136	2	2	math	math	PROPN
ma-136	2	3	.	.	PUNCT
ma-136	3	1	anal	anal	ADJ
ma-136	3	2	.	.	PUNCT
ma-136	4	1	3	3	NUM
ma-136	4	2	(	(	PUNCT
ma-136	4	3	2023	2023	NUM
ma-136	4	4	)	)	PUNCT
ma-136	4	5	10doi	10doi	NUM
ma-136	4	6	:	:	PUNCT
ma-136	4	7	10.28924	10.28924	NUM
ma-136	4	8	/	/	SYM
ma-136	4	9	ada	ada	NOUN
ma-136	4	10	/	/	SYM
ma-136	4	11	ma.3.10	ma.3.10	ADJ
ma-136	4	12	complex	complex	ADJ
ma-136	4	13	oscillation	oscillation	NOUN
ma-136	4	14	of	of	ADP
ma-136	4	15	solutions	solution	NOUN
ma-136	4	16	and	and	CCONJ
ma-136	4	17	their	their	PRON
ma-136	4	18	arbitrary	arbitrary	ADJ
ma-136	4	19	-	-	PUNCT
ma-136	4	20	order	order	NOUN
ma-136	4	21	derivatives	derivative	NOUN
ma-136	4	22	of	of	ADP
ma-136	4	23	linear	linear	ADJ
ma-136	4	24	differential	differential	ADJ
ma-136	4	25	equations	equation	NOUN
ma-136	4	26	with	with	ADP
ma-136	4	27	analytic	analytic	ADJ
ma-136	4	28	coefficients	coefficient	NOUN
ma-136	4	29	of	of	ADP
ma-136	4	30	[	[	X
ma-136	4	31	p	p	X
ma-136	4	32	,	,	PUNCT
ma-136	4	33	q]-order	q]-order	NOUN
ma-136	4	34	in	in	ADP
ma-136	4	35	the	the	DET
ma-136	4	36	unit	unit	NOUN
ma-136	4	37	disc	disc	PROPN
ma-136	4	38	benharrat	benharrat	PROPN
ma-136	4	39	belaïdi∗	belaïdi∗	PROPN
ma-136	4	40	,	,	PUNCT
ma-136	4	41	meriem	meriem	NOUN
ma-136	4	42	belmiloud	belmiloud	PROPN
ma-136	4	43	department	department	PROPN
ma-136	4	44	of	of	ADP
ma-136	4	45	mathematics	mathematic	NOUN
ma-136	4	46	,	,	PUNCT
ma-136	4	47	laboratory	laboratory	NOUN
ma-136	4	48	of	of	ADP
ma-136	4	49	pure	pure	ADJ
ma-136	4	50	and	and	CCONJ
ma-136	4	51	applied	applied	ADJ
ma-136	4	52	mathematics	mathematic	NOUN
ma-136	4	53	,	,	PUNCT
ma-136	4	54	university	university	NOUN
ma-136	4	55	of	of	ADP
ma-136	4	56	mostaganem	mostaganem	PROPN
ma-136	4	57	(	(	PUNCT
ma-136	4	58	umab	umab	NOUN
ma-136	4	59	)	)	PUNCT
ma-136	4	60	,	,	PUNCT
ma-136	5	1	b.	b.	PROPN
ma-136	5	2	p.	p.	NOUN
ma-136	5	3	227	227	NUM
ma-136	6	1	mostaganem	mostaganem	PROPN
ma-136	6	2	,	,	PUNCT
ma-136	6	3	algeria	algeria	PROPN
ma-136	6	4	benharrat.belaidi@univ-mosta.dz	benharrat.belaidi@univ-mosta.dz	PROPN
ma-136	6	5	,	,	PUNCT
ma-136	6	6	meriem.belmiloud27@gmail.com	meriem.belmiloud27@gmail.com	X
ma-136	6	7	∗correspondence	∗correspondence	NOUN
ma-136	6	8	:	:	PUNCT
ma-136	6	9	benharrat.belaidi@univ-mosta.dz	benharrat.belaidi@univ-mosta.dz	NOUN
ma-136	6	10	abstract	abstract	NOUN
ma-136	6	11	.	.	PUNCT
ma-136	7	1	throughout	throughout	ADP
ma-136	7	2	this	this	DET
ma-136	7	3	article	article	NOUN
ma-136	7	4	,	,	PUNCT
ma-136	7	5	we	we	PRON
ma-136	7	6	investigate	investigate	VERB
ma-136	7	7	the	the	DET
ma-136	7	8	growth	growth	NOUN
ma-136	7	9	and	and	CCONJ
ma-136	7	10	fixed	fix	VERB
ma-136	7	11	points	point	NOUN
ma-136	7	12	of	of	ADP
ma-136	7	13	solutions	solution	NOUN
ma-136	7	14	of	of	ADP
ma-136	7	15	complexhigher	complexhigher	NOUN
ma-136	7	16	order	order	NOUN
ma-136	7	17	linear	linear	PROPN
ma-136	7	18	differential	differential	NOUN
ma-136	7	19	equations	equation	NOUN
ma-136	7	20	in	in	ADP
ma-136	7	21	which	which	PRON
ma-136	7	22	the	the	DET
ma-136	7	23	coefficients	coefficient	NOUN
ma-136	7	24	are	be	AUX
ma-136	7	25	analytic	analytic	ADJ
ma-136	7	26	functions	function	NOUN
ma-136	7	27	of	of	ADP
ma-136	7	28	[	[	X
ma-136	7	29	p	p	X
ma-136	7	30	,	,	PUNCT
ma-136	7	31	q]−orderin	q]−orderin	VERB
ma-136	7	32	the	the	DET
ma-136	7	33	unit	unit	NOUN
ma-136	7	34	disc	disc	NOUN
ma-136	7	35	.	.	PUNCT
ma-136	8	1	this	this	DET
ma-136	8	2	work	work	NOUN
ma-136	8	3	improves	improve	VERB
ma-136	8	4	some	some	DET
ma-136	8	5	results	result	NOUN
ma-136	8	6	of	of	ADP
ma-136	8	7	belaïdi	belaïdi	NOUN
ma-136	8	8	[	[	X
ma-136	8	9	3–5	3–5	NOUN
ma-136	8	10	]	]	PUNCT
ma-136	8	11	,	,	PUNCT
ma-136	8	12	which	which	PRON
ma-136	8	13	is	be	AUX
ma-136	8	14	a	a	DET
ma-136	8	15	generalization	generalization	NOUN
ma-136	8	16	of	of	ADP
ma-136	8	17	recentresults	recentresult	NOUN
ma-136	8	18	from	from	ADP
ma-136	8	19	chen	chen	PROPN
ma-136	8	20	et	et	PROPN
ma-136	8	21	al	al	PROPN
ma-136	8	22	.	.	PUNCT
ma-136	9	1	[	[	X
ma-136	9	2	9	9	NUM
ma-136	9	3	]	]	SYM
ma-136	9	4	.	.	PUNCT
ma-136	10	1	1	1	X
ma-136	10	2	.	.	X
ma-136	10	3	introduction	introduction	NOUN
ma-136	10	4	and	and	CCONJ
ma-136	10	5	main	main	ADJ
ma-136	10	6	results	result	NOUN
ma-136	10	7	consider	consider	VERB
ma-136	10	8	for	for	ADP
ma-136	10	9	k	k	PROPN
ma-136	10	10	≥	≥	PROPN
ma-136	10	11	2	2	NUM
ma-136	10	12	the	the	DET
ma-136	10	13	following	follow	VERB
ma-136	10	14	complex	complex	ADJ
ma-136	10	15	linear	linear	ADJ
ma-136	10	16	differential	differential	NOUN
ma-136	10	17	equations	equation	NOUN
ma-136	10	18	f	f	X
ma-136	10	19	(	(	PUNCT
ma-136	10	20	k	k	NOUN
ma-136	10	21	)	)	PUNCT
ma-136	10	22	+	+	CCONJ
ma-136	10	23	ak−1	ak−1	ADV
ma-136	10	24	(	(	PUNCT
ma-136	10	25	z	z	NOUN
ma-136	10	26	)	)	PUNCT
ma-136	10	27	f	f	PROPN
ma-136	10	28	(	(	PUNCT
ma-136	10	29	k−1	k−1	PROPN
ma-136	10	30	)	)	PUNCT
ma-136	11	1	+	+	PUNCT
ma-136	11	2	·	·	PUNCT
ma-136	11	3	·	·	PUNCT
ma-136	11	4	·	·	PUNCT
ma-136	11	5	+	+	NUM
ma-136	11	6	a1	a1	NOUN
ma-136	11	7	(	(	PUNCT
ma-136	11	8	z	z	NOUN
ma-136	11	9	)	)	PUNCT
ma-136	11	10	f	f	NOUN
ma-136	11	11	′	′	NUM
ma-136	12	1	+	+	CCONJ
ma-136	12	2	a0	a0	PROPN
ma-136	12	3	(	(	PUNCT
ma-136	12	4	z	z	NOUN
ma-136	12	5	)	)	PUNCT
ma-136	12	6	f	f	NOUN
ma-136	13	1	=	=	SYM
ma-136	13	2	0	0	PROPN
ma-136	13	3	,	,	PUNCT
ma-136	13	4	(	(	PUNCT
ma-136	13	5	1.1	1.1	NUM
ma-136	13	6	)	)	PUNCT
ma-136	13	7	ak	ak	PROPN
ma-136	13	8	(	(	PUNCT
ma-136	13	9	z	z	PROPN
ma-136	13	10	)	)	PUNCT
ma-136	13	11	f	f	NOUN
ma-136	13	12	(	(	PUNCT
ma-136	13	13	k	k	NOUN
ma-136	13	14	)	)	PUNCT
ma-136	14	1	+	+	CCONJ
ma-136	14	2	ak−1	ak−1	ADV
ma-136	14	3	(	(	PUNCT
ma-136	14	4	z	z	NOUN
ma-136	14	5	)	)	PUNCT
ma-136	14	6	f	f	PROPN
ma-136	14	7	(	(	PUNCT
ma-136	14	8	k−1	k−1	PROPN
ma-136	14	9	)	)	PUNCT
ma-136	15	1	+	+	PUNCT
ma-136	15	2	·	·	PUNCT
ma-136	15	3	·	·	PUNCT
ma-136	15	4	·	·	PUNCT
ma-136	15	5	+	+	NUM
ma-136	15	6	a1	a1	NOUN
ma-136	15	7	(	(	PUNCT
ma-136	15	8	z	z	NOUN
ma-136	15	9	)	)	PUNCT
ma-136	15	10	f	f	NOUN
ma-136	15	11	′	′	NUM
ma-136	16	1	+	+	CCONJ
ma-136	16	2	a0	a0	PROPN
ma-136	16	3	(	(	PUNCT
ma-136	16	4	z	z	NOUN
ma-136	16	5	)	)	PUNCT
ma-136	16	6	f	f	NOUN
ma-136	17	1	=	=	SYM
ma-136	17	2	0	0	NUM
ma-136	17	3	,	,	PUNCT
ma-136	17	4	(	(	PUNCT
ma-136	17	5	1.2)where	1.2)where	NUM
ma-136	17	6	ai	ai	VERB
ma-136	17	7	6≡	6≡	NUM
ma-136	17	8	0	0	NUM
ma-136	18	1	(	(	PUNCT
ma-136	18	2	i	i	NOUN
ma-136	18	3	=	=	NOUN
ma-136	18	4	0	0	NUM
ma-136	18	5	,	,	PUNCT
ma-136	18	6	1	1	NUM
ma-136	18	7	,	,	PUNCT
ma-136	18	8	...	...	PUNCT
ma-136	18	9	,	,	PUNCT
ma-136	18	10	k	k	X
ma-136	18	11	)	)	PUNCT
ma-136	18	12	are	be	AUX
ma-136	18	13	analytic	analytic	ADJ
ma-136	18	14	functions	function	NOUN
ma-136	18	15	in	in	ADP
ma-136	18	16	the	the	DET
ma-136	18	17	unit	unit	NOUN
ma-136	18	18	disc	disc	VERB
ma-136	18	19	d	d	PROPN
ma-136	18	20	=	=	PUNCT
ma-136	18	21	{	{	PUNCT
ma-136	18	22	z	z	NOUN
ma-136	18	23	∈	∈	PROPN
ma-136	18	24	c	c	NOUN
ma-136	18	25	:	:	PUNCT
ma-136	19	1	|z	|z	PROPN
ma-136	20	1	|	|	ADV
ma-136	20	2	<	<	X
ma-136	20	3	1	1	NUM
ma-136	20	4	}	}	PUNCT
ma-136	20	5	.	.	PUNCT
ma-136	21	1	it	it	PRON
ma-136	21	2	iswell	iswell	NOUN
ma-136	21	3	-	-	PUNCT
ma-136	21	4	known	know	VERB
ma-136	21	5	that	that	SCONJ
ma-136	21	6	the	the	DET
ma-136	21	7	solutions	solution	NOUN
ma-136	21	8	of	of	ADP
ma-136	21	9	(	(	PUNCT
ma-136	21	10	1.1	1.1	NUM
ma-136	21	11	)	)	PUNCT
ma-136	21	12	are	be	AUX
ma-136	21	13	analytic	analytic	ADJ
ma-136	21	14	in	in	ADP
ma-136	21	15	d	d	PROPN
ma-136	21	16	too	too	ADV
ma-136	21	17	and	and	CCONJ
ma-136	21	18	that	that	SCONJ
ma-136	21	19	there	there	PRON
ma-136	21	20	are	be	VERB
ma-136	21	21	exactly	exactly	ADV
ma-136	21	22	k	k	X
ma-136	21	23	linearlyindependent	linearlyindependent	ADJ
ma-136	21	24	solutions	solution	NOUN
ma-136	21	25	of	of	ADP
ma-136	21	26	(	(	PUNCT
ma-136	21	27	1.1	1.1	NUM
ma-136	21	28	)	)	PUNCT
ma-136	21	29	,	,	PUNCT
ma-136	21	30	see	see	VERB
ma-136	21	31	[	[	X
ma-136	21	32	13	13	NUM
ma-136	21	33	]	]	PUNCT
ma-136	21	34	.	.	PUNCT
ma-136	22	1	bernal	bernal	PROPN
ma-136	23	1	[	[	X
ma-136	23	2	6	6	NUM
ma-136	23	3	]	]	PUNCT
ma-136	23	4	was	be	AUX
ma-136	23	5	the	the	DET
ma-136	23	6	first	first	ADJ
ma-136	23	7	to	to	PART
ma-136	23	8	use	use	VERB
ma-136	23	9	the	the	DET
ma-136	23	10	concept	concept	NOUN
ma-136	23	11	of	of	ADP
ma-136	23	12	iteratedorder	iteratedorder	NOUN
ma-136	23	13	to	to	PART
ma-136	23	14	study	study	VERB
ma-136	23	15	the	the	DET
ma-136	23	16	growth	growth	NOUN
ma-136	23	17	of	of	ADP
ma-136	23	18	fast	fast	ADJ
ma-136	23	19	growing	grow	VERB
ma-136	23	20	solutions	solution	NOUN
ma-136	23	21	of	of	ADP
ma-136	23	22	equation	equation	NOUN
ma-136	23	23	(	(	PUNCT
ma-136	23	24	1.1	1.1	NUM
ma-136	23	25	)	)	PUNCT
ma-136	23	26	.	.	PUNCT
ma-136	24	1	after	after	ADP
ma-136	24	2	that	that	PRON
ma-136	24	3	,	,	PUNCT
ma-136	24	4	the	the	DET
ma-136	24	5	iterated	iterated	ADJ
ma-136	24	6	orderof	orderof	NOUN
ma-136	24	7	solutions	solution	NOUN
ma-136	24	8	of	of	ADP
ma-136	24	9	higher	high	ADJ
ma-136	24	10	order	order	NOUN
ma-136	24	11	equations	equation	NOUN
ma-136	24	12	was	be	AUX
ma-136	24	13	investigated	investigate	VERB
ma-136	24	14	by	by	ADP
ma-136	24	15	cao	cao	PROPN
ma-136	24	16	in	in	ADP
ma-136	24	17	[	[	X
ma-136	24	18	8	8	NUM
ma-136	24	19	]	]	PUNCT
ma-136	24	20	,	,	PUNCT
ma-136	24	21	he	he	PRON
ma-136	24	22	extended	extend	VERB
ma-136	24	23	the	the	DET
ma-136	24	24	results	result	NOUN
ma-136	24	25	ofchen	ofchen	ADV
ma-136	24	26	and	and	CCONJ
ma-136	24	27	yang	yang	PROPN
ma-136	25	1	[	[	X
ma-136	25	2	10	10	NUM
ma-136	25	3	]	]	PUNCT
ma-136	25	4	,	,	PUNCT
ma-136	25	5	belaïdi	belaïdi	NOUN
ma-136	25	6	[	[	X
ma-136	25	7	2	2	X
ma-136	25	8	]	]	PUNCT
ma-136	25	9	on	on	ADP
ma-136	25	10	c.	c.	NOUN
ma-136	25	11	in	in	ADP
ma-136	25	12	addition	addition	NOUN
ma-136	25	13	,	,	PUNCT
ma-136	25	14	cao	cao	PROPN
ma-136	26	1	[	[	X
ma-136	26	2	8	8	NUM
ma-136	26	3	]	]	PUNCT
ma-136	26	4	obtained	obtain	VERB
ma-136	26	5	some	some	DET
ma-136	26	6	results	result	NOUN
ma-136	26	7	concerning	concern	VERB
ma-136	26	8	thefixed	thefixed	ADJ
ma-136	26	9	points	point	NOUN
ma-136	26	10	of	of	ADP
ma-136	26	11	homogeneous	homogeneous	ADJ
ma-136	26	12	linear	linear	PROPN
ma-136	26	13	differential	differential	NOUN
ma-136	26	14	equations	equation	NOUN
ma-136	26	15	(	(	PUNCT
ma-136	26	16	1.1	1.1	NUM
ma-136	26	17	)	)	PUNCT
ma-136	26	18	and	and	CCONJ
ma-136	26	19	(	(	PUNCT
ma-136	26	20	1.2	1.2	NUM
ma-136	26	21	)	)	PUNCT
ma-136	26	22	.	.	PUNCT
ma-136	27	1	in	in	ADP
ma-136	27	2	[	[	X
ma-136	27	3	15,16	15,16	NUM
ma-136	27	4	]	]	PUNCT
ma-136	27	5	,	,	PUNCT
ma-136	27	6	juneja	juneja	ADJ
ma-136	27	7	and	and	CCONJ
ma-136	27	8	hisco	hisco	NOUN
ma-136	27	9	-	-	NOUN
ma-136	27	10	authors	author	NOUN
ma-136	27	11	have	have	AUX
ma-136	27	12	investigated	investigate	VERB
ma-136	27	13	some	some	DET
ma-136	27	14	properties	property	NOUN
ma-136	27	15	of	of	ADP
ma-136	27	16	entire	entire	ADJ
ma-136	27	17	functions	function	NOUN
ma-136	27	18	of	of	ADP
ma-136	27	19	[	[	X
ma-136	27	20	p	p	X
ma-136	27	21	,	,	PUNCT
ma-136	27	22	q]-order	q]-order	NOUN
ma-136	27	23	,	,	PUNCT
ma-136	27	24	and	and	CCONJ
ma-136	27	25	obtained	obtain	VERB
ma-136	27	26	someresults	someresult	NOUN
ma-136	27	27	of	of	ADP
ma-136	27	28	their	their	PRON
ma-136	27	29	growth	growth	NOUN
ma-136	27	30	.	.	PUNCT
ma-136	28	1	in	in	ADP
ma-136	28	2	[	[	X
ma-136	28	3	20	20	NUM
ma-136	28	4	]	]	PUNCT
ma-136	28	5	,	,	PUNCT
ma-136	28	6	by	by	ADP
ma-136	28	7	using	use	VERB
ma-136	28	8	the	the	DET
ma-136	28	9	concept	concept	NOUN
ma-136	28	10	of	of	ADP
ma-136	28	11	[	[	X
ma-136	28	12	p	p	X
ma-136	28	13	,	,	PUNCT
ma-136	28	14	q]-order	q]-order	NOUN
ma-136	28	15	liu	liu	PROPN
ma-136	28	16	,	,	PUNCT
ma-136	28	17	tu	tu	PROPN
ma-136	28	18	and	and	CCONJ
ma-136	28	19	shi	shi	PROPN
ma-136	28	20	have	have	VERB
ma-136	28	21	consideredthe	consideredthe	ADJ
ma-136	28	22	equation	equation	NOUN
ma-136	28	23	(	(	PUNCT
ma-136	28	24	1.1	1.1	NUM
ma-136	28	25	)	)	PUNCT
ma-136	28	26	with	with	ADP
ma-136	28	27	entire	entire	ADJ
ma-136	28	28	coefficients	coefficient	NOUN
ma-136	28	29	and	and	CCONJ
ma-136	28	30	obtained	obtain	VERB
ma-136	28	31	different	different	ADJ
ma-136	28	32	results	result	NOUN
ma-136	28	33	concerning	concern	VERB
ma-136	28	34	the	the	DET
ma-136	28	35	growth	growth	NOUN
ma-136	28	36	of	of	ADP
ma-136	28	37	itssolutions	itssolution	NOUN
ma-136	28	38	in	in	ADP
ma-136	28	39	the	the	DET
ma-136	28	40	complex	complex	ADJ
ma-136	28	41	plane	plane	NOUN
ma-136	28	42	.	.	PUNCT
ma-136	29	1	in	in	ADP
ma-136	29	2	[	[	X
ma-136	29	3	3	3	NUM
ma-136	29	4	]	]	PUNCT
ma-136	29	5	,	,	PUNCT
ma-136	29	6	the	the	DET
ma-136	29	7	[	[	X
ma-136	29	8	p	p	X
ma-136	29	9	,	,	PUNCT
ma-136	29	10	q]−order	q]−order	PROPN
ma-136	29	11	was	be	AUX
ma-136	29	12	introduced	introduce	VERB
ma-136	29	13	in	in	ADP
ma-136	29	14	the	the	DET
ma-136	29	15	unit	unit	NOUN
ma-136	29	16	disc	disc	NOUN
ma-136	29	17	d	d	PROPN
ma-136	29	18	,	,	PUNCT
ma-136	29	19	and	and	CCONJ
ma-136	29	20	manyresults	manyresult	NOUN
ma-136	29	21	on	on	ADP
ma-136	29	22	[	[	X
ma-136	29	23	p	p	X
ma-136	29	24	,	,	PUNCT
ma-136	29	25	q]−order	q]−order	NOUN
ma-136	29	26	of	of	ADP
ma-136	29	27	solutions	solution	NOUN
ma-136	29	28	of	of	ADP
ma-136	29	29	(	(	PUNCT
ma-136	29	30	1.1	1.1	NUM
ma-136	29	31	)	)	PUNCT
ma-136	29	32	have	have	AUX
ma-136	29	33	been	be	AUX
ma-136	29	34	found	find	VERB
ma-136	29	35	by	by	ADP
ma-136	29	36	different	different	ADJ
ma-136	29	37	researchers	researcher	NOUN
ma-136	30	1	[	[	X
ma-136	30	2	3–5,14,18,22]in	3–5,14,18,22]in	NUM
ma-136	30	3	d.	d.	NOUN
ma-136	30	4	recently	recently	ADV
ma-136	30	5	,	,	PUNCT
ma-136	30	6	chen	chen	PROPN
ma-136	30	7	et	et	PROPN
ma-136	30	8	al	al	PROPN
ma-136	30	9	.	.	PUNCT
ma-136	31	1	in	in	ADP
ma-136	31	2	[	[	X
ma-136	31	3	9	9	NUM
ma-136	31	4	]	]	PUNCT
ma-136	31	5	gave	give	VERB
ma-136	31	6	some	some	DET
ma-136	31	7	results	result	NOUN
ma-136	31	8	about	about	ADP
ma-136	31	9	the	the	DET
ma-136	31	10	growth	growth	NOUN
ma-136	31	11	and	and	CCONJ
ma-136	31	12	fixed	fix	VERB
ma-136	31	13	points	point	NOUN
ma-136	31	14	of	of	ADP
ma-136	31	15	solutions	solution	NOUN
ma-136	31	16	received	receive	VERB
ma-136	31	17	:	:	PUNCT
ma-136	31	18	30	30	NUM
ma-136	31	19	sep	sep	NOUN
ma-136	31	20	2022	2022	NUM
ma-136	31	21	.	.	PUNCT
ma-136	32	1	key	key	ADJ
ma-136	32	2	words	word	NOUN
ma-136	32	3	and	and	CCONJ
ma-136	32	4	phrases	phrase	NOUN
ma-136	32	5	.	.	PUNCT
ma-136	33	1	linear	linear	ADJ
ma-136	33	2	differential	differential	ADJ
ma-136	33	3	equations	equation	NOUN
ma-136	33	4	;	;	PUNCT
ma-136	33	5	analytic	analytic	ADJ
ma-136	33	6	function	function	NOUN
ma-136	33	7	;	;	PUNCT
ma-136	34	1	[	[	X
ma-136	34	2	p	p	X
ma-136	34	3	,	,	PUNCT
ma-136	34	4	q]−order	q]−order	ADP
ma-136	34	5	;	;	PUNCT
ma-136	34	6	fixed	fix	VERB
ma-136	34	7	points.1	points.1	PROPN
ma-136	34	8	https://adac.ee	https://adac.ee	PROPN
ma-136	34	9	https://doi.org/10.28924/ada/ma.3.10	https://doi.org/10.28924/ada/ma.3.10	ADV
ma-136	34	10	eur	eur	NOUN
ma-136	34	11	.	.	PUNCT
ma-136	35	1	j.	j.	PROPN
ma-136	35	2	math	math	PROPN
ma-136	35	3	.	.	PUNCT
ma-136	36	1	anal	anal	PROPN
ma-136	36	2	.	.	PUNCT
ma-136	37	1	10.28924	10.28924	NUM
ma-136	37	2	/	/	SYM
ma-136	37	3	ada	ada	NOUN
ma-136	37	4	/	/	SYM
ma-136	37	5	ma.3.10	ma.3.10	ADJ
ma-136	37	6	2of	2of	NOUN
ma-136	37	7	higher	high	ADJ
ma-136	37	8	-	-	PUNCT
ma-136	37	9	order	order	NOUN
ma-136	37	10	linear	linear	ADJ
ma-136	37	11	differential	differential	NOUN
ma-136	37	12	equations	equation	NOUN
ma-136	37	13	in	in	ADP
ma-136	37	14	the	the	DET
ma-136	37	15	unit	unit	NOUN
ma-136	37	16	disc	disc	NOUN
ma-136	37	17	,	,	PUNCT
ma-136	37	18	they	they	PRON
ma-136	37	19	studied	study	VERB
ma-136	37	20	and	and	CCONJ
ma-136	37	21	estimated	estimate	VERB
ma-136	37	22	the	the	DET
ma-136	37	23	fixedpoints	fixedpoint	NOUN
ma-136	37	24	of	of	ADP
ma-136	37	25	solutions	solution	NOUN
ma-136	37	26	of	of	ADP
ma-136	37	27	(	(	PUNCT
ma-136	37	28	1.1	1.1	NUM
ma-136	37	29	)	)	PUNCT
ma-136	37	30	and	and	CCONJ
ma-136	37	31	(	(	PUNCT
ma-136	37	32	1.2	1.2	NUM
ma-136	37	33	)	)	PUNCT
ma-136	37	34	,	,	PUNCT
ma-136	37	35	and	and	CCONJ
ma-136	37	36	also	also	ADV
ma-136	37	37	extended	extend	VERB
ma-136	37	38	the	the	DET
ma-136	37	39	coefficient	coefficient	NOUN
ma-136	37	40	conditions	condition	NOUN
ma-136	37	41	to	to	ADP
ma-136	37	42	a	a	DET
ma-136	37	43	type	type	NOUN
ma-136	37	44	ofone	ofone	NOUN
ma-136	37	45	-	-	PUNCT
ma-136	37	46	constant	constant	ADJ
ma-136	37	47	-	-	PUNCT
ma-136	37	48	control	control	NOUN
ma-136	37	49	coefficient	coefficient	NOUN
ma-136	37	50	comparison	comparison	NOUN
ma-136	37	51	and	and	CCONJ
ma-136	37	52	obtained	obtain	VERB
ma-136	37	53	the	the	DET
ma-136	37	54	same	same	ADJ
ma-136	37	55	estimates	estimate	NOUN
ma-136	37	56	of	of	ADP
ma-136	37	57	iterated	iterated	ADJ
ma-136	37	58	order	order	NOUN
ma-136	37	59	ofsolutions	ofsolution	NOUN
ma-136	37	60	.	.	PUNCT
ma-136	38	1	the	the	DET
ma-136	38	2	aim	aim	NOUN
ma-136	38	3	of	of	ADP
ma-136	38	4	this	this	DET
ma-136	38	5	paper	paper	NOUN
ma-136	38	6	is	be	AUX
ma-136	38	7	to	to	PART
ma-136	38	8	contrast	contrast	VERB
ma-136	38	9	coefficients	coefficient	NOUN
ma-136	38	10	by	by	ADP
ma-136	38	11	producing	produce	VERB
ma-136	38	12	better	well	ADJ
ma-136	38	13	estimates	estimate	NOUN
ma-136	38	14	of	of	ADP
ma-136	38	15	thegrowth	thegrowth	NOUN
ma-136	38	16	of	of	ADP
ma-136	38	17	solutions	solution	NOUN
ma-136	38	18	by	by	ADP
ma-136	38	19	using	use	VERB
ma-136	38	20	the	the	DET
ma-136	38	21	concept	concept	NOUN
ma-136	38	22	of	of	ADP
ma-136	38	23	[	[	X
ma-136	38	24	p	p	X
ma-136	38	25	,	,	PUNCT
ma-136	38	26	q]−order	q]−order	ADP
ma-136	38	27	,	,	PUNCT
ma-136	38	28	and	and	CCONJ
ma-136	38	29	optimizing	optimize	VERB
ma-136	38	30	the	the	DET
ma-136	38	31	coefficients	coefficient	NOUN
ma-136	38	32	’s	’s	PART
ma-136	38	33	conditionswith	conditionswith	PROPN
ma-136	38	34	less	less	ADJ
ma-136	38	35	control	control	NOUN
ma-136	38	36	constants	constant	NOUN
ma-136	38	37	of	of	ADP
ma-136	38	38	the	the	DET
ma-136	38	39	coefficients	coefficient	NOUN
ma-136	38	40	’s	’s	PART
ma-136	38	41	modulus	modulus	ADJ
ma-136	38	42	or	or	CCONJ
ma-136	38	43	characteristic	characteristic	ADJ
ma-136	38	44	functions	function	NOUN
ma-136	38	45	and	and	CCONJ
ma-136	38	46	we	we	PRON
ma-136	38	47	will	will	AUX
ma-136	38	48	obtainresults	obtainresult	NOUN
ma-136	38	49	which	which	PRON
ma-136	38	50	improve	improve	VERB
ma-136	38	51	and	and	CCONJ
ma-136	38	52	generalize	generalize	VERB
ma-136	38	53	those	those	PRON
ma-136	38	54	of	of	ADP
ma-136	38	55	chen	chen	PROPN
ma-136	38	56	et	et	PROPN
ma-136	38	57	al	al	PROPN
ma-136	38	58	.	.	PROPN
ma-136	38	59	,	,	PUNCT
ma-136	38	60	belaïdi	belaïdi	PROPN
ma-136	38	61	,	,	PUNCT
ma-136	38	62	cao	cao	PROPN
ma-136	38	63	,	,	PUNCT
ma-136	38	64	tu	tu	PROPN
ma-136	38	65	and	and	CCONJ
ma-136	38	66	xuan	xuan	PROPN
ma-136	38	67	.	.	PUNCT
ma-136	39	1	throughout	throughout	ADP
ma-136	39	2	this	this	DET
ma-136	39	3	paper	paper	NOUN
ma-136	39	4	,	,	PUNCT
ma-136	39	5	we	we	PRON
ma-136	39	6	shall	shall	AUX
ma-136	39	7	assume	assume	VERB
ma-136	39	8	that	that	SCONJ
ma-136	39	9	the	the	DET
ma-136	39	10	reader	reader	NOUN
ma-136	39	11	is	be	AUX
ma-136	39	12	familiar	familiar	ADJ
ma-136	39	13	with	with	ADP
ma-136	39	14	the	the	DET
ma-136	39	15	fundamental	fundamental	ADJ
ma-136	39	16	resultsand	resultsand	NOUN
ma-136	39	17	the	the	DET
ma-136	39	18	standard	standard	ADJ
ma-136	39	19	notations	notation	NOUN
ma-136	39	20	of	of	ADP
ma-136	39	21	the	the	DET
ma-136	39	22	nevanlinna	nevanlinna	NOUN
ma-136	39	23	’s	’s	PART
ma-136	39	24	theory	theory	NOUN
ma-136	39	25	in	in	ADP
ma-136	39	26	the	the	DET
ma-136	39	27	unit	unit	NOUN
ma-136	39	28	disc	disc	VERB
ma-136	39	29	d	d	PROPN
ma-136	39	30	=	=	PUNCT
ma-136	39	31	{	{	PUNCT
ma-136	39	32	z	z	NOUN
ma-136	39	33	∈	∈	PROPN
ma-136	39	34	c	c	NOUN
ma-136	39	35	:	:	PUNCT
ma-136	39	36	|z	|z	PROPN
ma-136	40	1	|	|	ADV
ma-136	40	2	<	<	X
ma-136	40	3	1}(see	1}(see	NUM
ma-136	40	4	,	,	PUNCT
ma-136	40	5	[	[	X
ma-136	40	6	12	12	NUM
ma-136	40	7	,	,	PUNCT
ma-136	40	8	13,17,21	13,17,21	NUM
ma-136	40	9	]	]	PUNCT
ma-136	40	10	)	)	PUNCT
ma-136	40	11	.	.	PUNCT
ma-136	41	1	now	now	ADV
ma-136	41	2	,	,	PUNCT
ma-136	41	3	we	we	PRON
ma-136	41	4	give	give	VERB
ma-136	41	5	the	the	DET
ma-136	41	6	definitions	definition	NOUN
ma-136	41	7	of	of	ADP
ma-136	41	8	iterated	iterated	ADJ
ma-136	41	9	order	order	NOUN
ma-136	41	10	and	and	CCONJ
ma-136	41	11	growth	growth	NOUN
ma-136	41	12	index	index	NOUN
ma-136	41	13	to	to	PART
ma-136	41	14	classify	classify	VERB
ma-136	41	15	generally	generally	ADV
ma-136	41	16	thefunctions	thefunction	NOUN
ma-136	41	17	of	of	ADP
ma-136	41	18	fast	fast	ADJ
ma-136	41	19	growth	growth	NOUN
ma-136	41	20	in	in	ADP
ma-136	41	21	d	d	PROPN
ma-136	41	22	as	as	ADP
ma-136	41	23	those	those	PRON
ma-136	41	24	in	in	ADP
ma-136	41	25	c	c	PROPN
ma-136	41	26	(	(	PUNCT
ma-136	41	27	see	see	VERB
ma-136	41	28	,	,	PUNCT
ma-136	41	29	[	[	X
ma-136	41	30	6	6	NUM
ma-136	41	31	]	]	PUNCT
ma-136	41	32	)	)	PUNCT
ma-136	41	33	.	.	PUNCT
ma-136	42	1	let	let	VERB
ma-136	42	2	us	we	PRON
ma-136	42	3	define	define	VERB
ma-136	42	4	inductively	inductively	ADV
ma-136	42	5	,	,	PUNCT
ma-136	42	6	for	for	ADP
ma-136	42	7	r	r	NOUN
ma-136	42	8	∈	∈	PROPN
ma-136	42	9	r	r	NOUN
ma-136	42	10	,	,	PUNCT
ma-136	42	11	exp1	exp1	ADJ
ma-136	42	12	r	r	NOUN
ma-136	42	13	:	:	PUNCT
ma-136	42	14	=	=	PUNCT
ma-136	42	15	erand	erand	NOUN
ma-136	42	16	expp+1	expp+1	NOUN
ma-136	43	1	r	r	NOUN
ma-136	43	2	:	:	PUNCT
ma-136	43	3	=	=	SYM
ma-136	43	4	exp	exp	X
ma-136	43	5	(	(	PUNCT
ma-136	43	6	expp	expp	ADJ
ma-136	43	7	r	r	NOUN
ma-136	43	8	)	)	PUNCT
ma-136	43	9	,	,	PUNCT
ma-136	43	10	p	p	PROPN
ma-136	43	11	∈	∈	PROPN
ma-136	43	12	n.	n.	NOUN
ma-136	43	13	we	we	PRON
ma-136	43	14	also	also	ADV
ma-136	43	15	define	define	VERB
ma-136	43	16	for	for	ADP
ma-136	43	17	all	all	DET
ma-136	43	18	r	r	NOUN
ma-136	43	19	sufficiently	sufficiently	ADV
ma-136	43	20	large	large	ADJ
ma-136	43	21	in	in	ADP
ma-136	43	22	(	(	PUNCT
ma-136	43	23	0,+∞	0,+∞	NUM
ma-136	43	24	)	)	PUNCT
ma-136	43	25	,	,	PUNCT
ma-136	43	26	log1	log1	PROPN
ma-136	43	27	r	r	NOUN
ma-136	43	28	:	:	PUNCT
ma-136	43	29	=	=	PUNCT
ma-136	43	30	log	log	NOUN
ma-136	43	31	r	r	NOUN
ma-136	43	32	and	and	CCONJ
ma-136	43	33	logp+1	logp+1	NOUN
ma-136	43	34	r	r	NOUN
ma-136	43	35	:	:	PUNCT
ma-136	43	36	=	=	NOUN
ma-136	43	37	log	log	NOUN
ma-136	43	38	(	(	PUNCT
ma-136	43	39	logp	logp	NOUN
ma-136	43	40	r	r	NOUN
ma-136	43	41	)	)	PUNCT
ma-136	43	42	,	,	PUNCT
ma-136	43	43	p	p	PROPN
ma-136	43	44	∈	∈	PROPN
ma-136	43	45	n.	n.	NOUN
ma-136	43	46	moreover	moreover	ADV
ma-136	43	47	,	,	PUNCT
ma-136	43	48	we	we	PRON
ma-136	43	49	denote	denote	VERB
ma-136	43	50	by	by	ADP
ma-136	43	51	exp0	exp0	PROPN
ma-136	43	52	r	r	NOUN
ma-136	43	53	:	:	PUNCT
ma-136	43	54	=	=	SYM
ma-136	43	55	r	r	NOUN
ma-136	43	56	,	,	PUNCT
ma-136	43	57	log0	log0	ADJ
ma-136	43	58	r	r	NOUN
ma-136	43	59	:	:	PUNCT
ma-136	43	60	=	=	SYM
ma-136	43	61	r	r	NOUN
ma-136	43	62	,	,	PUNCT
ma-136	43	63	log−1	log−1	PROPN
ma-136	43	64	r	r	NOUN
ma-136	43	65	:	:	PUNCT
ma-136	43	66	=	=	SYM
ma-136	43	67	exp1	exp1	PROPN
ma-136	43	68	r	r	NOUN
ma-136	43	69	and	and	CCONJ
ma-136	43	70	exp−1	exp−1	PROPN
ma-136	43	71	r	r	NOUN
ma-136	43	72	:	:	PUNCT
ma-136	43	73	=	=	SYM
ma-136	43	74	log1	log1	PROPN
ma-136	43	75	r.	r.	PROPN
ma-136	43	76	definition	definition	NOUN
ma-136	43	77	1.1	1.1	NUM
ma-136	43	78	(	(	PUNCT
ma-136	43	79	see	see	VERB
ma-136	43	80	[	[	X
ma-136	43	81	7	7	NUM
ma-136	43	82	]	]	PUNCT
ma-136	43	83	)	)	PUNCT
ma-136	43	84	let	let	VERB
ma-136	43	85	f	f	PRON
ma-136	43	86	be	be	AUX
ma-136	43	87	a	a	DET
ma-136	43	88	meromorphic	meromorphic	ADJ
ma-136	43	89	function	function	NOUN
ma-136	43	90	in	in	ADP
ma-136	43	91	d.	d.	PROPN
ma-136	43	92	then	then	ADV
ma-136	43	93	the	the	DET
ma-136	43	94	iterated	iterated	ADJ
ma-136	43	95	n−order	n−order	NOUN
ma-136	43	96	of	of	ADP
ma-136	43	97	f	f	PROPN
ma-136	43	98	is	be	AUX
ma-136	43	99	defined	define	VERB
ma-136	43	100	by	by	ADP
ma-136	43	101	σn	σn	X
ma-136	43	102	(	(	PUNCT
ma-136	43	103	f	f	NOUN
ma-136	43	104	)	)	PUNCT
ma-136	44	1	=	=	SYM
ma-136	44	2	lim	lim	PROPN
ma-136	44	3	sup	sup	PROPN
ma-136	44	4	r→1−	r→1−	PROPN
ma-136	44	5	log+n	log+n	PROPN
ma-136	44	6	t	t	PROPN
ma-136	44	7	(	(	PUNCT
ma-136	44	8	r	r	PROPN
ma-136	44	9	,	,	PUNCT
ma-136	44	10	f	f	PROPN
ma-136	44	11	)	)	PUNCT
ma-136	44	12	log	log	NOUN
ma-136	44	13	(	(	PUNCT
ma-136	44	14	1	1	NUM
ma-136	44	15	1−r	1−r	NUM
ma-136	44	16	)	)	PUNCT
ma-136	44	17	(	(	PUNCT
ma-136	44	18	n	n	CCONJ
ma-136	44	19	≥	≥	NOUN
ma-136	44	20	1	1	NUM
ma-136	44	21	is	be	AUX
ma-136	44	22	an	an	DET
ma-136	44	23	integer	integer	NOUN
ma-136	44	24	)	)	PUNCT
ma-136	44	25	,	,	PUNCT
ma-136	44	26	where	where	SCONJ
ma-136	44	27	log+1	log+1	X
ma-136	44	28	x	x	PUNCT
ma-136	45	1	=	=	PUNCT
ma-136	45	2	log+	log+	ADJ
ma-136	45	3	x	x	X
ma-136	45	4	=	=	SYM
ma-136	45	5	max	max	PROPN
ma-136	45	6	{	{	PUNCT
ma-136	45	7	log	log	NOUN
ma-136	45	8	x	x	X
ma-136	45	9	,	,	PUNCT
ma-136	45	10	0	0	NUM
ma-136	45	11	}	}	PUNCT
ma-136	45	12	,	,	PUNCT
ma-136	45	13	log+n+1	log+n+1	PROPN
ma-136	45	14	x	x	X
ma-136	46	1	=	=	PUNCT
ma-136	46	2	log+	log+	ADJ
ma-136	46	3	(	(	PUNCT
ma-136	46	4	log+n	log+n	PROPN
ma-136	46	5	x	x	X
ma-136	46	6	)	)	PUNCT
ma-136	46	7	.	.	PUNCT
ma-136	47	1	for	for	ADP
ma-136	47	2	n	n	NOUN
ma-136	47	3	=	=	SYM
ma-136	47	4	1	1	NUM
ma-136	47	5	,	,	PUNCT
ma-136	47	6	this	this	DET
ma-136	47	7	notation	notation	NOUN
ma-136	47	8	is	be	AUX
ma-136	47	9	called	call	VERB
ma-136	47	10	order	order	NOUN
ma-136	47	11	(	(	PUNCT
ma-136	47	12	σ1	σ1	NOUN
ma-136	47	13	(	(	PUNCT
ma-136	47	14	f	f	PROPN
ma-136	47	15	)	)	PUNCT
ma-136	48	1	=	=	SYM
ma-136	48	2	σ	σ	PROPN
ma-136	48	3	(	(	PUNCT
ma-136	48	4	f	f	PROPN
ma-136	48	5	)	)	PUNCT
ma-136	48	6	)	)	PUNCT
ma-136	48	7	and	and	CCONJ
ma-136	48	8	for	for	ADP
ma-136	48	9	n	n	NOUN
ma-136	48	10	=	=	SYM
ma-136	48	11	2	2	NUM
ma-136	48	12	hyper	hyper	NOUN
ma-136	48	13	-	-	NOUN
ma-136	48	14	order	order	NOUN
ma-136	48	15	(	(	PUNCT
ma-136	48	16	[	[	X
ma-136	48	17	19	19	NUM
ma-136	48	18	]	]	NUM
ma-136	48	19	)	)	PUNCT
ma-136	48	20	.	.	PUNCT
ma-136	49	1	if	if	SCONJ
ma-136	49	2	f	f	PROPN
ma-136	49	3	is	be	AUX
ma-136	49	4	an	an	DET
ma-136	49	5	analytic	analytic	NOUN
ma-136	49	6	in	in	ADP
ma-136	49	7	d	d	PROPN
ma-136	49	8	,	,	PUNCT
ma-136	49	9	then	then	ADV
ma-136	49	10	the	the	DET
ma-136	49	11	iterated	iterated	ADJ
ma-136	49	12	n−order	n−order	NOUN
ma-136	49	13	of	of	ADP
ma-136	49	14	f	f	PROPN
ma-136	49	15	is	be	AUX
ma-136	49	16	defined	define	VERB
ma-136	49	17	by	by	ADP
ma-136	49	18	σm	σm	X
ma-136	49	19	,	,	PUNCT
ma-136	49	20	n	n	PROPN
ma-136	49	21	(	(	PUNCT
ma-136	49	22	f	f	X
ma-136	49	23	)	)	PUNCT
ma-136	50	1	=	=	SYM
ma-136	50	2	lim	lim	PROPN
ma-136	50	3	sup	sup	PROPN
ma-136	50	4	r→1−	r→1−	PROPN
ma-136	50	5	log+n+1	log+n+1	PROPN
ma-136	50	6	m	m	PROPN
ma-136	50	7	(	(	PUNCT
ma-136	50	8	r	r	NOUN
ma-136	50	9	,	,	PUNCT
ma-136	50	10	f	f	PROPN
ma-136	50	11	)	)	PUNCT
ma-136	50	12	log	log	NOUN
ma-136	50	13	(	(	PUNCT
ma-136	50	14	1	1	NUM
ma-136	50	15	1−r	1−r	NUM
ma-136	50	16	)	)	PUNCT
ma-136	50	17	(	(	PUNCT
ma-136	50	18	n	n	CCONJ
ma-136	50	19	≥	≥	NOUN
ma-136	50	20	1	1	NUM
ma-136	50	21	is	be	AUX
ma-136	50	22	an	an	DET
ma-136	50	23	integer	integer	NOUN
ma-136	50	24	)	)	PUNCT
ma-136	50	25	.	.	PUNCT
ma-136	51	1	for	for	ADP
ma-136	51	2	n	n	NOUN
ma-136	51	3	=	=	SYM
ma-136	51	4	1	1	NUM
ma-136	51	5	,	,	PUNCT
ma-136	51	6	σm,1	σm,1	PROPN
ma-136	51	7	(	(	PUNCT
ma-136	51	8	f	f	PROPN
ma-136	51	9	)	)	PUNCT
ma-136	51	10	=	=	SYM
ma-136	51	11	σm	σm	X
ma-136	51	12	(	(	PUNCT
ma-136	51	13	f	f	PROPN
ma-136	51	14	)	)	PUNCT
ma-136	51	15	.	.	PUNCT
ma-136	52	1	now	now	ADV
ma-136	52	2	,	,	PUNCT
ma-136	52	3	we	we	PRON
ma-136	52	4	introduce	introduce	VERB
ma-136	52	5	the	the	DET
ma-136	52	6	concept	concept	NOUN
ma-136	52	7	of	of	ADP
ma-136	52	8	[	[	X
ma-136	52	9	p	p	X
ma-136	52	10	,	,	PUNCT
ma-136	52	11	q]-order	q]-order	NOUN
ma-136	52	12	of	of	ADP
ma-136	52	13	meromorphic	meromorphic	ADJ
ma-136	52	14	and	and	CCONJ
ma-136	52	15	analytic	analytic	ADJ
ma-136	52	16	functions	function	NOUN
ma-136	52	17	in	in	ADP
ma-136	52	18	theunit	theunit	VERB
ma-136	52	19	disc	disc	NOUN
ma-136	52	20	.	.	PUNCT
ma-136	53	1	definition	definition	NOUN
ma-136	53	2	1.2	1.2	NUM
ma-136	53	3	(	(	PUNCT
ma-136	53	4	[	[	X
ma-136	53	5	3	3	NUM
ma-136	53	6	]	]	PUNCT
ma-136	53	7	)	)	PUNCT
ma-136	53	8	let	let	VERB
ma-136	53	9	p	p	PRON
ma-136	53	10	≥	≥	PRON
ma-136	53	11	q	q	NOUN
ma-136	53	12	≥	≥	NUM
ma-136	53	13	1	1	NUM
ma-136	53	14	be	be	AUX
ma-136	53	15	integers	integer	NOUN
ma-136	53	16	and	and	CCONJ
ma-136	53	17	f	f	PROPN
ma-136	53	18	be	be	AUX
ma-136	53	19	a	a	DET
ma-136	53	20	meromorphic	meromorphic	ADJ
ma-136	53	21	function	function	NOUN
ma-136	53	22	in	in	ADP
ma-136	53	23	d.	d.	PROPN
ma-136	53	24	then	then	ADV
ma-136	53	25	,	,	PUNCT
ma-136	54	1	the	the	DET
ma-136	54	2	[	[	AUX
ma-136	54	3	p	p	X
ma-136	54	4	,	,	PUNCT
ma-136	54	5	q]-order	q]-order	NOUN
ma-136	54	6	of	of	ADP
ma-136	54	7	f	f	PROPN
ma-136	54	8	is	be	AUX
ma-136	54	9	defined	define	VERB
ma-136	54	10	by	by	ADP
ma-136	54	11	σ[p	σ[p	NOUN
ma-136	54	12	,	,	PUNCT
ma-136	54	13	q	q	X
ma-136	54	14	]	]	X
ma-136	54	15	(	(	PUNCT
ma-136	54	16	f	f	X
ma-136	54	17	)	)	PUNCT
ma-136	55	1	=	=	SYM
ma-136	55	2	lim	lim	PROPN
ma-136	55	3	sup	sup	PROPN
ma-136	55	4	r→1−	r→1−	PROPN
ma-136	55	5	log+p	log+p	PROPN
ma-136	55	6	t	t	PROPN
ma-136	55	7	(	(	PUNCT
ma-136	55	8	r	r	NOUN
ma-136	55	9	,	,	PUNCT
ma-136	55	10	f	f	NOUN
ma-136	55	11	)	)	PUNCT
ma-136	55	12	logq	logq	NOUN
ma-136	55	13	(	(	PUNCT
ma-136	55	14	1	1	NUM
ma-136	55	15	1−r	1−r	NUM
ma-136	55	16	)	)	PUNCT
ma-136	55	17	.	.	PUNCT
ma-136	56	1	https://doi.org/10.28924/ada/ma.3.10	https://doi.org/10.28924/ada/ma.3.10	ADV
ma-136	56	2	eur	eur	PROPN
ma-136	56	3	.	.	PUNCT
ma-136	57	1	j.	j.	PROPN
ma-136	57	2	math	math	PROPN
ma-136	57	3	.	.	PUNCT
ma-136	58	1	anal	anal	PROPN
ma-136	58	2	.	.	PUNCT
ma-136	59	1	10.28924	10.28924	NUM
ma-136	59	2	/	/	SYM
ma-136	59	3	ada	ada	NOUN
ma-136	59	4	/	/	SYM
ma-136	59	5	ma.3.10	ma.3.10	NOUN
ma-136	59	6	3	3	NUM
ma-136	59	7	for	for	ADP
ma-136	59	8	an	an	DET
ma-136	59	9	analytic	analytic	ADJ
ma-136	59	10	function	function	NOUN
ma-136	59	11	f	f	PROPN
ma-136	59	12	in	in	ADP
ma-136	59	13	d	d	PROPN
ma-136	59	14	,	,	PUNCT
ma-136	59	15	we	we	PRON
ma-136	59	16	also	also	ADV
ma-136	59	17	define	define	VERB
ma-136	59	18	σm,[p	σm,[p	NOUN
ma-136	59	19	,	,	PUNCT
ma-136	59	20	q	q	X
ma-136	59	21	]	]	X
ma-136	59	22	(	(	PUNCT
ma-136	59	23	f	f	X
ma-136	59	24	)	)	PUNCT
ma-136	60	1	=	=	SYM
ma-136	60	2	lim	lim	PROPN
ma-136	60	3	sup	sup	PROPN
ma-136	60	4	r→1−	r→1−	PROPN
ma-136	60	5	log+p+1	log+p+1	PROPN
ma-136	60	6	m	m	PROPN
ma-136	60	7	(	(	PUNCT
ma-136	60	8	r	r	NOUN
ma-136	60	9	,	,	PUNCT
ma-136	60	10	f	f	NOUN
ma-136	60	11	)	)	PUNCT
ma-136	60	12	logq	logq	NOUN
ma-136	60	13	(	(	PUNCT
ma-136	60	14	1	1	NUM
ma-136	60	15	1−r	1−r	NUM
ma-136	60	16	)	)	PUNCT
ma-136	60	17	.	.	PUNCT
ma-136	61	1	remark	remark	VERB
ma-136	61	2	1.1	1.1	NUM
ma-136	61	3	it	it	PRON
ma-136	61	4	is	be	AUX
ma-136	61	5	easy	easy	ADJ
ma-136	61	6	to	to	PART
ma-136	61	7	see	see	VERB
ma-136	61	8	that	that	SCONJ
ma-136	61	9	0	0	NUM
ma-136	61	10	≤	≤	NUM
ma-136	61	11	σ[p	σ[p	NOUN
ma-136	61	12	,	,	PUNCT
ma-136	61	13	q	q	X
ma-136	61	14	]	]	X
ma-136	61	15	(	(	PUNCT
ma-136	61	16	f	f	PROPN
ma-136	61	17	)	)	PUNCT
ma-136	62	1	≤	≤	NOUN
ma-136	62	2	∞	∞	PROPN
ma-136	62	3	(	(	PUNCT
ma-136	62	4	0	0	NUM
ma-136	62	5	≤	≤	NUM
ma-136	62	6	σm,[p	σm,[p	NOUN
ma-136	62	7	,	,	PUNCT
ma-136	62	8	q	q	X
ma-136	62	9	]	]	X
ma-136	62	10	(	(	PUNCT
ma-136	62	11	f	f	PROPN
ma-136	62	12	)	)	PUNCT
ma-136	62	13	≤	≤	NOUN
ma-136	62	14	∞	∞	NUM
ma-136	62	15	)	)	PUNCT
ma-136	62	16	,	,	PUNCT
ma-136	62	17	for	for	ADP
ma-136	62	18	any	any	DET
ma-136	62	19	p	p	PROPN
ma-136	62	20	≥	≥	NOUN
ma-136	62	21	q	q	NOUN
ma-136	62	22	≥	≥	NUM
ma-136	62	23	1	1	NUM
ma-136	62	24	.	.	PUNCT
ma-136	63	1	by	by	ADP
ma-136	63	2	definition	definition	NOUN
ma-136	63	3	1.2	1.2	NUM
ma-136	63	4	,	,	PUNCT
ma-136	63	5	we	we	PRON
ma-136	63	6	have	have	VERB
ma-136	63	7	that	that	DET
ma-136	63	8	σ[1,1	σ[1,1	NOUN
ma-136	63	9	]	]	PUNCT
ma-136	64	1	=	=	SYM
ma-136	64	2	σ	σ	PROPN
ma-136	64	3	(	(	PUNCT
ma-136	64	4	f	f	PROPN
ma-136	64	5	)	)	PUNCT
ma-136	64	6	(	(	PUNCT
ma-136	64	7	σm,[1,1	σm,[1,1	NOUN
ma-136	64	8	]	]	X
ma-136	64	9	=	=	PUNCT
ma-136	64	10	σm	σm	X
ma-136	64	11	(	(	PUNCT
ma-136	64	12	f	f	PROPN
ma-136	64	13	)	)	PUNCT
ma-136	64	14	)	)	PUNCT
ma-136	64	15	and	and	CCONJ
ma-136	64	16	σ[2,1	σ[2,1	NOUN
ma-136	64	17	]	]	PUNCT
ma-136	64	18	=	=	SYM
ma-136	64	19	σ2	σ2	PROPN
ma-136	64	20	(	(	PUNCT
ma-136	64	21	f	f	PROPN
ma-136	64	22	)	)	PUNCT
ma-136	64	23	(	(	PUNCT
ma-136	64	24	σm,[2,1	σm,[2,1	X
ma-136	64	25	]	]	X
ma-136	64	26	=	=	PUNCT
ma-136	64	27	σm,2	σm,2	PROPN
ma-136	64	28	(	(	PUNCT
ma-136	64	29	f	f	PROPN
ma-136	64	30	)	)	PUNCT
ma-136	64	31	)	)	PUNCT
ma-136	64	32	.	.	PUNCT
ma-136	65	1	proposition	proposition	NOUN
ma-136	65	2	1.1	1.1	NUM
ma-136	65	3	(	(	PUNCT
ma-136	65	4	[	[	X
ma-136	65	5	3	3	NUM
ma-136	65	6	]	]	PUNCT
ma-136	65	7	)	)	PUNCT
ma-136	65	8	let	let	VERB
ma-136	65	9	p	p	PRON
ma-136	65	10	≥	≥	PRON
ma-136	65	11	q	q	NOUN
ma-136	65	12	≥	≥	NUM
ma-136	65	13	1	1	NUM
ma-136	65	14	be	be	VERB
ma-136	65	15	integers	integer	NOUN
ma-136	65	16	,	,	PUNCT
ma-136	65	17	and	and	CCONJ
ma-136	65	18	let	let	VERB
ma-136	65	19	f	f	PRON
ma-136	65	20	be	be	AUX
ma-136	65	21	an	an	DET
ma-136	65	22	analytic	analytic	ADJ
ma-136	65	23	function	function	NOUN
ma-136	65	24	in	in	ADP
ma-136	65	25	d	d	PROPN
ma-136	65	26	of	of	ADP
ma-136	65	27	[	[	X
ma-136	65	28	p	p	X
ma-136	65	29	,	,	PUNCT
ma-136	65	30	q]-order	q]-order	NOUN
ma-136	65	31	.	.	PUNCT
ma-136	66	1	the	the	DET
ma-136	66	2	following	follow	VERB
ma-136	66	3	two	two	NUM
ma-136	66	4	statements	statement	NOUN
ma-136	66	5	hold	hold	VERB
ma-136	66	6	:	:	PUNCT
ma-136	66	7	(	(	PUNCT
ma-136	66	8	i	i	NOUN
ma-136	66	9	)	)	PUNCT
ma-136	66	10	if	if	SCONJ
ma-136	66	11	p	p	NOUN
ma-136	66	12	=	=	NOUN
ma-136	66	13	q	q	ADJ
ma-136	66	14	,	,	PUNCT
ma-136	66	15	then	then	ADV
ma-136	66	16	σ[p	σ[p	NOUN
ma-136	66	17	,	,	PUNCT
ma-136	66	18	q	q	X
ma-136	66	19	]	]	X
ma-136	66	20	(	(	PUNCT
ma-136	66	21	f	f	PROPN
ma-136	66	22	)	)	PUNCT
ma-136	66	23	≤	≤	NOUN
ma-136	66	24	σm,[p	σm,[p	NOUN
ma-136	66	25	,	,	PUNCT
ma-136	66	26	q	q	X
ma-136	66	27	]	]	X
ma-136	66	28	(	(	PUNCT
ma-136	66	29	f	f	PROPN
ma-136	66	30	)	)	PUNCT
ma-136	66	31	≤	≤	NOUN
ma-136	66	32	σ[p	σ[p	NOUN
ma-136	66	33	,	,	PUNCT
ma-136	66	34	q	q	X
ma-136	66	35	]	]	X
ma-136	66	36	(	(	PUNCT
ma-136	66	37	f	f	X
ma-136	66	38	)	)	PUNCT
ma-136	67	1	+	+	CCONJ
ma-136	67	2	1	1	X
ma-136	67	3	.	.	X
ma-136	67	4	(	(	PUNCT
ma-136	67	5	ii	ii	NOUN
ma-136	67	6	)	)	PUNCT
ma-136	67	7	if	if	SCONJ
ma-136	67	8	p	p	PROPN
ma-136	67	9	>	>	X
ma-136	67	10	q	q	X
ma-136	67	11	,	,	PUNCT
ma-136	67	12	then	then	ADV
ma-136	67	13	σ[p	σ[p	NOUN
ma-136	67	14	,	,	PUNCT
ma-136	67	15	q	q	X
ma-136	67	16	]	]	X
ma-136	67	17	(	(	PUNCT
ma-136	67	18	f	f	X
ma-136	67	19	)	)	PUNCT
ma-136	67	20	=	=	SYM
ma-136	67	21	σm,[p	σm,[p	NOUN
ma-136	67	22	,	,	PUNCT
ma-136	67	23	q	q	X
ma-136	67	24	]	]	X
ma-136	67	25	(	(	PUNCT
ma-136	67	26	f	f	PROPN
ma-136	67	27	)	)	PUNCT
ma-136	67	28	.	.	PUNCT
ma-136	68	1	definition	definition	NOUN
ma-136	68	2	1.3	1.3	NUM
ma-136	68	3	(	(	PUNCT
ma-136	68	4	[	[	X
ma-136	68	5	4	4	NUM
ma-136	68	6	]	]	PUNCT
ma-136	68	7	)	)	PUNCT
ma-136	68	8	let	let	VERB
ma-136	68	9	p	p	PRON
ma-136	68	10	≥	≥	PRON
ma-136	68	11	q	q	NOUN
ma-136	68	12	≥	≥	NUM
ma-136	68	13	1	1	NUM
ma-136	68	14	be	be	AUX
ma-136	68	15	integers	integer	NOUN
ma-136	68	16	and	and	CCONJ
ma-136	68	17	f	f	PROPN
ma-136	68	18	be	be	AUX
ma-136	68	19	a	a	DET
ma-136	68	20	meromorphic	meromorphic	ADJ
ma-136	68	21	function	function	NOUN
ma-136	68	22	in	in	ADP
ma-136	68	23	d.	d.	PROPN
ma-136	68	24	then	then	ADV
ma-136	68	25	,	,	PUNCT
ma-136	68	26	the	the	PRON
ma-136	68	27	[	[	AUX
ma-136	68	28	p	p	X
ma-136	68	29	,	,	PUNCT
ma-136	68	30	q]-exponent	q]-exponent	NOUN
ma-136	68	31	of	of	ADP
ma-136	68	32	convergence	convergence	NOUN
ma-136	68	33	of	of	ADP
ma-136	68	34	the	the	DET
ma-136	68	35	sequence	sequence	NOUN
ma-136	68	36	of	of	ADP
ma-136	68	37	zeros	zero	NOUN
ma-136	68	38	of	of	ADP
ma-136	68	39	f	f	PROPN
ma-136	68	40	is	be	AUX
ma-136	68	41	defined	define	VERB
ma-136	68	42	by	by	ADP
ma-136	68	43	λ[p	λ[p	PROPN
ma-136	68	44	,	,	PUNCT
ma-136	68	45	q	q	X
ma-136	68	46	]	]	X
ma-136	68	47	(	(	PUNCT
ma-136	68	48	f	f	X
ma-136	68	49	)	)	PUNCT
ma-136	69	1	=	=	SYM
ma-136	69	2	lim	lim	PROPN
ma-136	69	3	sup	sup	PROPN
ma-136	69	4	r→1−	r→1−	PROPN
ma-136	69	5	log+p	log+p	NUM
ma-136	69	6	n	n	CCONJ
ma-136	69	7	(	(	PUNCT
ma-136	69	8	r	r	NOUN
ma-136	69	9	,	,	PUNCT
ma-136	69	10	1f	1f	NUM
ma-136	69	11	)	)	PUNCT
ma-136	69	12	logq	logq	NOUN
ma-136	69	13	(	(	PUNCT
ma-136	69	14	1	1	NUM
ma-136	69	15	1−r	1−r	NUM
ma-136	69	16	)	)	PUNCT
ma-136	69	17	,	,	PUNCT
ma-136	69	18	where	where	SCONJ
ma-136	69	19	n	n	X
ma-136	69	20	(	(	PUNCT
ma-136	69	21	r	r	NOUN
ma-136	69	22	,	,	PUNCT
ma-136	69	23	1f	1f	NUM
ma-136	69	24	)	)	PUNCT
ma-136	69	25	is	be	AUX
ma-136	69	26	the	the	DET
ma-136	69	27	integrated	integrate	VERB
ma-136	69	28	counting	counting	NOUN
ma-136	69	29	function	function	NOUN
ma-136	69	30	of	of	ADP
ma-136	69	31	zeros	zero	NOUN
ma-136	69	32	of	of	ADP
ma-136	69	33	f	f	PROPN
ma-136	69	34	in	in	ADP
ma-136	69	35	{	{	PUNCT
ma-136	69	36	z	z	NOUN
ma-136	69	37	:	:	PUNCT
ma-136	69	38	|z	|z	PROPN
ma-136	70	1	|	|	ADV
ma-136	70	2	≤	≤	X
ma-136	70	3	r	r	NOUN
ma-136	70	4	}	}	PUNCT
ma-136	70	5	.	.	PUNCT
ma-136	71	1	similarly	similarly	ADV
ma-136	71	2	,	,	PUNCT
ma-136	71	3	the	the	PRON
ma-136	71	4	[	[	AUX
ma-136	71	5	p	p	X
ma-136	71	6	,	,	PUNCT
ma-136	71	7	q]-exponent	q]-exponent	NOUN
ma-136	71	8	of	of	ADP
ma-136	71	9	convergence	convergence	NOUN
ma-136	71	10	of	of	ADP
ma-136	71	11	the	the	DET
ma-136	71	12	sequence	sequence	NOUN
ma-136	71	13	of	of	ADP
ma-136	71	14	distinct	distinct	ADJ
ma-136	71	15	zeros	zero	NOUN
ma-136	71	16	of	of	ADP
ma-136	71	17	f	f	PROPN
ma-136	71	18	is	be	AUX
ma-136	71	19	defined	define	VERB
ma-136	71	20	by	by	ADP
ma-136	71	21	λ[p	λ[p	PROPN
ma-136	71	22	,	,	PUNCT
ma-136	71	23	q	q	X
ma-136	71	24	]	]	X
ma-136	71	25	(	(	PUNCT
ma-136	71	26	f	f	X
ma-136	71	27	)	)	PUNCT
ma-136	72	1	=	=	SYM
ma-136	72	2	lim	lim	PROPN
ma-136	72	3	sup	sup	PROPN
ma-136	72	4	r→1−	r→1−	PROPN
ma-136	72	5	log+p	log+p	NUM
ma-136	72	6	n	n	CCONJ
ma-136	72	7	(	(	PUNCT
ma-136	72	8	r	r	NOUN
ma-136	72	9	,	,	PUNCT
ma-136	72	10	1f	1f	NUM
ma-136	72	11	)	)	PUNCT
ma-136	72	12	logq	logq	VERB
ma-136	72	13	1	1	NUM
ma-136	72	14	1−r	1−r	NUM
ma-136	72	15	,	,	PUNCT
ma-136	72	16	where	where	SCONJ
ma-136	72	17	n	n	X
ma-136	72	18	(	(	PUNCT
ma-136	72	19	r	r	NOUN
ma-136	72	20	,	,	PUNCT
ma-136	72	21	1f	1f	NUM
ma-136	72	22	)	)	PUNCT
ma-136	72	23	is	be	AUX
ma-136	72	24	the	the	DET
ma-136	72	25	integrated	integrate	VERB
ma-136	72	26	counting	counting	NOUN
ma-136	72	27	function	function	NOUN
ma-136	72	28	of	of	ADP
ma-136	72	29	distinct	distinct	ADJ
ma-136	72	30	zeros	zero	NOUN
ma-136	72	31	of	of	ADP
ma-136	72	32	f	f	PROPN
ma-136	72	33	in	in	ADP
ma-136	72	34	{	{	PUNCT
ma-136	72	35	z	z	NOUN
ma-136	72	36	:	:	PUNCT
ma-136	72	37	|z	|z	PROPN
ma-136	73	1	|	|	ADV
ma-136	73	2	≤	≤	X
ma-136	73	3	r	r	NOUN
ma-136	73	4	}	}	PUNCT
ma-136	73	5	.	.	PUNCT
ma-136	74	1	definition	definition	NOUN
ma-136	74	2	1.4	1.4	NUM
ma-136	74	3	let	let	VERB
ma-136	74	4	p	p	PRON
ma-136	74	5	≥	≥	PRON
ma-136	74	6	q	q	NOUN
ma-136	74	7	≥	≥	NUM
ma-136	74	8	1	1	NUM
ma-136	74	9	be	be	AUX
ma-136	74	10	integers	integer	NOUN
ma-136	74	11	and	and	CCONJ
ma-136	74	12	f	f	PROPN
ma-136	74	13	be	be	AUX
ma-136	74	14	a	a	DET
ma-136	74	15	meromorphic	meromorphic	ADJ
ma-136	74	16	function	function	NOUN
ma-136	74	17	in	in	ADP
ma-136	74	18	d.	d.	PROPN
ma-136	74	19	then	then	ADV
ma-136	74	20	,	,	PUNCT
ma-136	74	21	the	the	PRON
ma-136	74	22	[	[	AUX
ma-136	74	23	p	p	X
ma-136	74	24	,	,	PUNCT
ma-136	74	25	q]-exponent	q]-exponent	NOUN
ma-136	74	26	of	of	ADP
ma-136	74	27	convergence	convergence	NOUN
ma-136	74	28	of	of	ADP
ma-136	74	29	the	the	DET
ma-136	74	30	sequence	sequence	NOUN
ma-136	74	31	of	of	ADP
ma-136	74	32	fixed	fix	VERB
ma-136	74	33	points	point	NOUN
ma-136	74	34	of	of	ADP
ma-136	74	35	f	f	PROPN
ma-136	74	36	is	be	AUX
ma-136	74	37	defined	define	VERB
ma-136	74	38	by	by	ADP
ma-136	74	39	λ[p	λ[p	PROPN
ma-136	74	40	,	,	PUNCT
ma-136	74	41	q	q	X
ma-136	74	42	]	]	X
ma-136	74	43	(	(	PUNCT
ma-136	74	44	f	f	PROPN
ma-136	74	45	−	−	PROPN
ma-136	74	46	z	z	PROPN
ma-136	74	47	)	)	PUNCT
ma-136	75	1	=	=	SYM
ma-136	75	2	lim	lim	PROPN
ma-136	75	3	sup	sup	PROPN
ma-136	75	4	r→1−	r→1−	PROPN
ma-136	75	5	log+p	log+p	NUM
ma-136	75	6	n	n	CCONJ
ma-136	75	7	(	(	PUNCT
ma-136	75	8	r	r	NOUN
ma-136	75	9	,	,	PUNCT
ma-136	75	10	1f−z	1f−z	NOUN
ma-136	75	11	)	)	PUNCT
ma-136	75	12	logq	logq	NOUN
ma-136	75	13	(	(	PUNCT
ma-136	75	14	1	1	NUM
ma-136	75	15	1−r	1−r	NUM
ma-136	75	16	)	)	PUNCT
ma-136	75	17	.	.	PUNCT
ma-136	76	1	similarly	similarly	ADV
ma-136	76	2	,	,	PUNCT
ma-136	76	3	the	the	PRON
ma-136	76	4	[	[	AUX
ma-136	76	5	p	p	X
ma-136	76	6	,	,	PUNCT
ma-136	76	7	q]-exponent	q]-exponent	NOUN
ma-136	76	8	of	of	ADP
ma-136	76	9	convergence	convergence	NOUN
ma-136	76	10	of	of	ADP
ma-136	76	11	the	the	DET
ma-136	76	12	sequence	sequence	NOUN
ma-136	76	13	of	of	ADP
ma-136	76	14	distinct	distinct	ADJ
ma-136	76	15	fixed	fix	VERB
ma-136	76	16	points	point	NOUN
ma-136	76	17	of	of	ADP
ma-136	76	18	f	f	PROPN
ma-136	76	19	is	be	AUX
ma-136	76	20	defined	define	VERB
ma-136	76	21	by	by	ADP
ma-136	76	22	λ̄[p	λ̄[p	PROPN
ma-136	76	23	,	,	PUNCT
ma-136	76	24	q	q	X
ma-136	76	25	]	]	X
ma-136	76	26	(	(	PUNCT
ma-136	76	27	f	f	PROPN
ma-136	76	28	−	−	PROPN
ma-136	76	29	z	z	PROPN
ma-136	76	30	)	)	PUNCT
ma-136	76	31	=	=	SYM
ma-136	76	32	lim	lim	PROPN
ma-136	76	33	sup	sup	PROPN
ma-136	76	34	r→1−	r→1−	PROPN
ma-136	76	35	log+p	log+p	PROPN
ma-136	76	36	n̄	n̄	NOUN
ma-136	76	37	(	(	PUNCT
ma-136	76	38	r	r	NOUN
ma-136	76	39	,	,	PUNCT
ma-136	76	40	1f−z	1f−z	NOUN
ma-136	76	41	)	)	PUNCT
ma-136	76	42	logq	logq	NOUN
ma-136	76	43	(	(	PUNCT
ma-136	76	44	1	1	NUM
ma-136	76	45	1−r	1−r	NUM
ma-136	76	46	)	)	PUNCT
ma-136	76	47	.	.	PUNCT
ma-136	77	1	recall	recall	VERB
ma-136	77	2	that	that	PRON
ma-136	77	3	for	for	ADP
ma-136	77	4	a	a	DET
ma-136	77	5	measurable	measurable	ADJ
ma-136	77	6	set	set	NOUN
ma-136	77	7	e	e	PROPN
ma-136	77	8	⊂	⊂	PROPN
ma-136	78	1	[	[	X
ma-136	78	2	0	0	NUM
ma-136	78	3	,	,	PUNCT
ma-136	78	4	1	1	NUM
ma-136	78	5	)	)	PUNCT
ma-136	78	6	,	,	PUNCT
ma-136	78	7	the	the	DET
ma-136	78	8	upper	upper	ADJ
ma-136	78	9	and	and	CCONJ
ma-136	78	10	lower	low	ADJ
ma-136	78	11	densities	density	NOUN
ma-136	78	12	of	of	ADP
ma-136	78	13	e	e	NOUN
ma-136	78	14	are	be	AUX
ma-136	78	15	defined	define	VERB
ma-136	78	16	by	by	ADP
ma-136	78	17	densde	densde	NOUN
ma-136	78	18	=	=	SYM
ma-136	78	19	lim	lim	PROPN
ma-136	78	20	sup	sup	PROPN
ma-136	78	21	r→1−	r→1−	PROPN
ma-136	78	22	m	m	PROPN
ma-136	78	23	(	(	PUNCT
ma-136	78	24	e	e	X
ma-136	78	25	∩	∩	X
ma-136	78	26	[	[	X
ma-136	78	27	0	0	NUM
ma-136	78	28	,	,	PUNCT
ma-136	78	29	r	r	NOUN
ma-136	78	30	)	)	PUNCT
ma-136	78	31	)	)	PUNCT
ma-136	79	1	m	m	VERB
ma-136	79	2	(	(	PUNCT
ma-136	79	3	[	[	X
ma-136	79	4	0	0	NUM
ma-136	79	5	,	,	PUNCT
ma-136	79	6	r	r	NOUN
ma-136	79	7	)	)	PUNCT
ma-136	79	8	)	)	PUNCT
ma-136	80	1	and	and	CCONJ
ma-136	80	2	densde	densde	PRON
ma-136	80	3	=	=	SYM
ma-136	80	4	lim	lim	PROPN
ma-136	80	5	inf	inf	PROPN
ma-136	80	6	r→1−	r→1−	PROPN
ma-136	80	7	m	m	PROPN
ma-136	80	8	(	(	PUNCT
ma-136	80	9	e	e	X
ma-136	80	10	∩	∩	X
ma-136	80	11	[	[	X
ma-136	80	12	0	0	NUM
ma-136	80	13	,	,	PUNCT
ma-136	80	14	r	r	NOUN
ma-136	80	15	)	)	PUNCT
ma-136	80	16	)	)	PUNCT
ma-136	81	1	m	m	VERB
ma-136	81	2	(	(	PUNCT
ma-136	81	3	[	[	X
ma-136	81	4	0	0	NUM
ma-136	81	5	,	,	PUNCT
ma-136	81	6	r	r	NOUN
ma-136	81	7	)	)	PUNCT
ma-136	81	8	)	)	PUNCT
ma-136	81	9	,	,	PUNCT
ma-136	81	10	respectively	respectively	ADV
ma-136	81	11	,	,	PUNCT
ma-136	81	12	where	where	SCONJ
ma-136	81	13	m	m	VERB
ma-136	81	14	(	(	PUNCT
ma-136	81	15	f	f	X
ma-136	81	16	)	)	PUNCT
ma-136	81	17	=	=	PUNCT
ma-136	82	1	∫	∫	PROPN
ma-136	82	2	f	f	PROPN
ma-136	82	3	dt	dt	PROPN
ma-136	82	4	1−t	1−t	NUM
ma-136	82	5	for	for	ADP
ma-136	82	6	f	f	PROPN
ma-136	82	7	⊂	⊂	PROPN
ma-136	83	1	[	[	X
ma-136	83	2	0	0	NUM
ma-136	83	3	,	,	PUNCT
ma-136	83	4	1	1	NUM
ma-136	83	5	)	)	PUNCT
ma-136	83	6	.	.	PUNCT
ma-136	84	1	it	it	PRON
ma-136	84	2	is	be	AUX
ma-136	84	3	clear	clear	ADJ
ma-136	84	4	that	that	SCONJ
ma-136	84	5	0	0	NUM
ma-136	84	6	≤	≤	NUM
ma-136	84	7	densde	densde	NOUN
ma-136	84	8	≤	≤	NUM
ma-136	84	9	densde	densde	NOUN
ma-136	84	10	≤	≤	NOUN
ma-136	85	1	1for	1for	ADP
ma-136	86	1	any	any	DET
ma-136	86	2	measurable	measurable	ADJ
ma-136	86	3	set	set	NOUN
ma-136	86	4	e	e	PROPN
ma-136	86	5	⊂	⊂	PROPN
ma-136	87	1	[	[	X
ma-136	87	2	0	0	NUM
ma-136	87	3	,	,	PUNCT
ma-136	87	4	1	1	NUM
ma-136	87	5	)	)	PUNCT
ma-136	87	6	.	.	PUNCT
ma-136	88	1	https://doi.org/10.28924/ada/ma.3.10	https://doi.org/10.28924/ada/ma.3.10	ADV
ma-136	88	2	eur	eur	PROPN
ma-136	88	3	.	.	PUNCT
ma-136	89	1	j.	j.	PROPN
ma-136	89	2	math	math	PROPN
ma-136	89	3	.	.	PUNCT
ma-136	90	1	anal	anal	PROPN
ma-136	90	2	.	.	PUNCT
ma-136	91	1	10.28924	10.28924	NUM
ma-136	91	2	/	/	SYM
ma-136	91	3	ada	ada	NOUN
ma-136	91	4	/	/	SYM
ma-136	91	5	ma.3.10	ma.3.10	ADJ
ma-136	91	6	4	4	NUM
ma-136	91	7	proposition	proposition	NOUN
ma-136	91	8	1.2	1.2	NUM
ma-136	91	9	if	if	SCONJ
ma-136	91	10	a	a	DET
ma-136	91	11	set	set	NOUN
ma-136	91	12	e	e	NOUN
ma-136	91	13	satisfies	satisfy	VERB
ma-136	91	14	densde	densde	PRON
ma-136	91	15	>	>	X
ma-136	91	16	0	0	PROPN
ma-136	91	17	,	,	PUNCT
ma-136	91	18	then	then	ADV
ma-136	91	19	m	m	VERB
ma-136	91	20	(	(	PUNCT
ma-136	91	21	e	e	NOUN
ma-136	91	22	)	)	PUNCT
ma-136	91	23	=	=	SYM
ma-136	92	1	∫	∫	PUNCT
ma-136	92	2	e	e	X
ma-136	92	3	dt	dt	NOUN
ma-136	92	4	1−t	1−t	NUM
ma-136	92	5	=	=	PUNCT
ma-136	93	1	+	+	NUM
ma-136	93	2	∞.	∞.	PROPN
ma-136	93	3	proof	proof	NOUN
ma-136	93	4	.	.	PUNCT
ma-136	93	5	suppose	suppose	VERB
ma-136	93	6	that	that	SCONJ
ma-136	93	7	m	m	VERB
ma-136	93	8	(	(	PUNCT
ma-136	93	9	e	e	NOUN
ma-136	93	10	)	)	PUNCT
ma-136	93	11	=	=	SYM
ma-136	93	12	∫	∫	PUNCT
ma-136	93	13	e	e	X
ma-136	93	14	dt	dt	NOUN
ma-136	93	15	1−t	1−t	NUM
ma-136	93	16	=	=	SYM
ma-136	93	17	δ	δ	PROPN
ma-136	93	18	<	<	X
ma-136	93	19	∞.	∞.	PROPN
ma-136	93	20	we	we	PRON
ma-136	93	21	have	have	VERB
ma-136	93	22	m	m	PRON
ma-136	93	23	(	(	PUNCT
ma-136	93	24	[	[	X
ma-136	93	25	0	0	NUM
ma-136	93	26	,	,	PUNCT
ma-136	93	27	r	r	NOUN
ma-136	93	28	)	)	PUNCT
ma-136	93	29	)	)	PUNCT
ma-136	94	1	=	=	SYM
ma-136	95	1	−	−	PROPN
ma-136	95	2	log	log	NOUN
ma-136	95	3	(	(	PUNCT
ma-136	95	4	1−	1−	NUM
ma-136	95	5	r	r	NOUN
ma-136	95	6	)	)	PUNCT
ma-136	95	7	.	.	PUNCT
ma-136	96	1	since	since	SCONJ
ma-136	96	2	m	m	PROPN
ma-136	96	3	(	(	PUNCT
ma-136	96	4	e	e	X
ma-136	96	5	∩	∩	X
ma-136	96	6	[	[	X
ma-136	96	7	0	0	NUM
ma-136	96	8	,	,	PUNCT
ma-136	96	9	r	r	NOUN
ma-136	96	10	)	)	PUNCT
ma-136	96	11	)	)	PUNCT
ma-136	96	12	≤	≤	NUM
ma-136	97	1	m	m	VERB
ma-136	97	2	(	(	PUNCT
ma-136	97	3	e	e	NOUN
ma-136	97	4	)	)	PUNCT
ma-136	97	5	,	,	PUNCT
ma-136	97	6	then	then	ADV
ma-136	97	7	densde	densde	NOUN
ma-136	97	8	=	=	SYM
ma-136	97	9	lim	lim	PROPN
ma-136	97	10	sup	sup	PROPN
ma-136	97	11	r→1−	r→1−	PROPN
ma-136	97	12	m	m	PROPN
ma-136	97	13	(	(	PUNCT
ma-136	97	14	e	e	X
ma-136	97	15	∩	∩	X
ma-136	97	16	[	[	X
ma-136	97	17	0	0	NUM
ma-136	97	18	,	,	PUNCT
ma-136	97	19	r	r	NOUN
ma-136	97	20	)	)	PUNCT
ma-136	97	21	)	)	PUNCT
ma-136	97	22	m	m	VERB
ma-136	97	23	(	(	PUNCT
ma-136	97	24	[	[	X
ma-136	97	25	0	0	NUM
ma-136	97	26	,	,	PUNCT
ma-136	97	27	r	r	NOUN
ma-136	97	28	)	)	PUNCT
ma-136	97	29	)	)	PUNCT
ma-136	97	30	≤	≤	NOUN
ma-136	97	31	lim	lim	PROPN
ma-136	97	32	sup	sup	PROPN
ma-136	97	33	r→1−	r→1−	PROPN
ma-136	97	34	δ	δ	PROPN
ma-136	97	35	−	−	PROPN
ma-136	97	36	log	log	NOUN
ma-136	97	37	(	(	PUNCT
ma-136	97	38	1−	1−	NUM
ma-136	97	39	r	r	NOUN
ma-136	97	40	)	)	PUNCT
ma-136	97	41	=	=	SYM
ma-136	97	42	0	0	X
ma-136	97	43	.	.	PUNCT
ma-136	98	1	so	so	ADV
ma-136	98	2	densde	densde	ADJ
ma-136	98	3	=	=	NOUN
ma-136	98	4	0	0	X
ma-136	98	5	.	.	PUNCT
ma-136	99	1	hence	hence	ADV
ma-136	99	2	densde	densde	X
ma-136	99	3	>	>	X
ma-136	99	4	0	0	PUNCT
ma-136	100	1	=	=	NOUN
ma-136	100	2	⇒	⇒	NOUN
ma-136	100	3	m	m	VERB
ma-136	100	4	(	(	PUNCT
ma-136	100	5	e	e	NOUN
ma-136	100	6	)	)	PUNCT
ma-136	100	7	=	=	SYM
ma-136	101	1	∫	∫	PUNCT
ma-136	101	2	e	e	X
ma-136	101	3	dt	dt	NOUN
ma-136	101	4	1−	1−	NUM
ma-136	101	5	t	t	NOUN
ma-136	101	6	=	=	PUNCT
ma-136	102	1	+	+	NUM
ma-136	102	2	∞.	∞.	PROPN
ma-136	102	3	in	in	ADP
ma-136	102	4	2012	2012	NUM
ma-136	102	5	,	,	PUNCT
ma-136	102	6	belaïdi	belaïdi	NOUN
ma-136	102	7	in	in	ADP
ma-136	102	8	[	[	X
ma-136	102	9	4	4	NUM
ma-136	102	10	]	]	PUNCT
ma-136	102	11	and	and	CCONJ
ma-136	102	12	[	[	X
ma-136	102	13	5	5	NUM
ma-136	102	14	]	]	PUNCT
ma-136	102	15	treated	treat	VERB
ma-136	102	16	the	the	DET
ma-136	102	17	growth	growth	NOUN
ma-136	102	18	of	of	ADP
ma-136	102	19	solutions	solution	NOUN
ma-136	102	20	of	of	ADP
ma-136	102	21	homogeneous	homogeneous	ADJ
ma-136	102	22	linear	linear	PROPN
ma-136	102	23	differentialequations	differentialequation	NOUN
ma-136	102	24	in	in	ADP
ma-136	102	25	which	which	PRON
ma-136	102	26	the	the	DET
ma-136	102	27	coefficients	coefficient	NOUN
ma-136	102	28	are	be	AUX
ma-136	102	29	analytic	analytic	ADJ
ma-136	102	30	functions	function	NOUN
ma-136	102	31	of	of	ADP
ma-136	102	32	[	[	X
ma-136	102	33	p	p	X
ma-136	102	34	,	,	PUNCT
ma-136	102	35	q]−order	q]−order	NOUN
ma-136	102	36	in	in	ADP
ma-136	102	37	d.	d.	PROPN
ma-136	102	38	as	as	ADP
ma-136	102	39	for	for	ADP
ma-136	102	40	the	the	DET
ma-136	102	41	equation	equation	NOUN
ma-136	102	42	(	(	PUNCT
ma-136	102	43	1.1	1.1	NUM
ma-136	102	44	)	)	PUNCT
ma-136	102	45	,	,	PUNCT
ma-136	102	46	he	he	PRON
ma-136	102	47	got	get	VERB
ma-136	102	48	the	the	DET
ma-136	102	49	following	follow	VERB
ma-136	102	50	results	result	NOUN
ma-136	102	51	.	.	PUNCT
ma-136	103	1	theorem	theorem	VERB
ma-136	103	2	a	a	PRON
ma-136	103	3	(	(	PUNCT
ma-136	103	4	see	see	VERB
ma-136	103	5	[	[	X
ma-136	103	6	4	4	NUM
ma-136	103	7	]	]	PUNCT
ma-136	103	8	)	)	PUNCT
ma-136	103	9	let	let	VERB
ma-136	103	10	p	p	PRON
ma-136	103	11	≥	≥	PRON
ma-136	103	12	q	q	NOUN
ma-136	103	13	≥	≥	NUM
ma-136	103	14	1	1	NUM
ma-136	103	15	be	be	AUX
ma-136	103	16	integers	integer	NOUN
ma-136	103	17	.	.	PUNCT
ma-136	104	1	let	let	VERB
ma-136	104	2	h	h	PRON
ma-136	104	3	be	be	AUX
ma-136	104	4	a	a	DET
ma-136	104	5	set	set	NOUN
ma-136	104	6	of	of	ADP
ma-136	104	7	complex	complex	ADJ
ma-136	104	8	numbers	number	NOUN
ma-136	104	9	satisfying	satisfy	VERB
ma-136	104	10	densd	densd	PROPN
ma-136	104	11	{	{	PUNCT
ma-136	104	12	|z	|z	PROPN
ma-136	105	1	|	|	ADV
ma-136	105	2	:	:	PUNCT
ma-136	105	3	z	z	PROPN
ma-136	105	4	∈	∈	PROPN
ma-136	105	5	h	h	NOUN
ma-136	106	1	⊆	⊆	NUM
ma-136	106	2	d	d	X
ma-136	106	3	}	}	PUNCT
ma-136	106	4	>	>	X
ma-136	106	5	0	0	NUM
ma-136	106	6	,	,	PUNCT
ma-136	106	7	and	and	CCONJ
ma-136	106	8	let	let	VERB
ma-136	106	9	a0	a0	PROPN
ma-136	106	10	(	(	PUNCT
ma-136	106	11	z	z	NOUN
ma-136	106	12	)	)	PUNCT
ma-136	106	13	,	,	PUNCT
ma-136	106	14	...	...	PUNCT
ma-136	106	15	,	,	PUNCT
ma-136	106	16	ak−1	ak−1	INTJ
ma-136	106	17	(	(	PUNCT
ma-136	106	18	z	z	NOUN
ma-136	106	19	)	)	PUNCT
ma-136	106	20	be	be	AUX
ma-136	106	21	analytic	analytic	ADJ
ma-136	106	22	functions	function	NOUN
ma-136	106	23	in	in	ADP
ma-136	106	24	the	the	DET
ma-136	106	25	unit	unit	NOUN
ma-136	106	26	disc	disc	VERB
ma-136	106	27	d	d	PROPN
ma-136	106	28	such	such	ADJ
ma-136	106	29	that	that	PRON
ma-136	106	30	for	for	ADP
ma-136	106	31	real	real	ADJ
ma-136	106	32	constants	constant	NOUN
ma-136	106	33	α	α	NOUN
ma-136	106	34	,	,	PUNCT
ma-136	106	35	β	β	NOUN
ma-136	106	36	,	,	PUNCT
ma-136	106	37	where	where	SCONJ
ma-136	106	38	0	0	NUM
ma-136	106	39	≤	≤	NOUN
ma-136	106	40	β	β	X
ma-136	106	41	<	<	X
ma-136	106	42	α	α	X
ma-136	106	43	,	,	PUNCT
ma-136	106	44	we	we	PRON
ma-136	106	45	have	have	VERB
ma-136	106	46	|a0	|a0	PROPN
ma-136	106	47	(	(	PUNCT
ma-136	106	48	z)|	z)|	PRON
ma-136	106	49	≥	≥	NOUN
ma-136	106	50	expp+1	expp+1	PROPN
ma-136	106	51	{	{	PUNCT
ma-136	106	52	α	α	PRON
ma-136	106	53	logq	logq	NOUN
ma-136	106	54	(	(	PUNCT
ma-136	106	55	1	1	NUM
ma-136	106	56	1−	1−	NUM
ma-136	106	57	|z	|z	NOUN
ma-136	106	58	|	|	ADV
ma-136	106	59	)	)	PUNCT
ma-136	106	60	}	}	PUNCT
ma-136	106	61	and	and	CCONJ
ma-136	106	62	|ai	|ai	NUM
ma-136	106	63	(	(	PUNCT
ma-136	106	64	z)|	z)|	ADP
ma-136	106	65	≤	≤	PROPN
ma-136	106	66	expp+1	expp+1	PROPN
ma-136	106	67	{	{	PUNCT
ma-136	106	68	β	β	X
ma-136	106	69	logq	logq	NOUN
ma-136	106	70	(	(	PUNCT
ma-136	106	71	1	1	NUM
ma-136	106	72	1−	1−	NUM
ma-136	106	73	|z	|z	NOUN
ma-136	106	74	|	|	ADV
ma-136	106	75	)	)	PUNCT
ma-136	106	76	}	}	PUNCT
ma-136	106	77	(	(	PUNCT
ma-136	106	78	i	i	NOUN
ma-136	106	79	=	=	NOUN
ma-136	106	80	1	1	NUM
ma-136	106	81	,	,	PUNCT
ma-136	106	82	...	...	PUNCT
ma-136	106	83	,	,	PUNCT
ma-136	106	84	k	k	PROPN
ma-136	107	1	−	−	PROPN
ma-136	107	2	1	1	NUM
ma-136	107	3	)	)	PUNCT
ma-136	107	4	as	as	ADP
ma-136	107	5	|z	|z	PROPN
ma-136	107	6	|	|	PROPN
ma-136	107	7	→	→	SYM
ma-136	107	8	1−	1−	NUM
ma-136	107	9	for	for	ADP
ma-136	107	10	z	z	PROPN
ma-136	107	11	∈	∈	PROPN
ma-136	107	12	h.	h.	NOUN
ma-136	107	13	then	then	ADV
ma-136	107	14	every	every	DET
ma-136	107	15	solution	solution	NOUN
ma-136	107	16	f	f	PROPN
ma-136	107	17	6≡	6≡	NUM
ma-136	107	18	0	0	NUM
ma-136	107	19	of	of	ADP
ma-136	107	20	equation	equation	NOUN
ma-136	107	21	(	(	PUNCT
ma-136	107	22	1.1	1.1	NUM
ma-136	107	23	)	)	PUNCT
ma-136	107	24	satisfies	satisfy	VERB
ma-136	107	25	σ[p	σ[p	NOUN
ma-136	107	26	,	,	PUNCT
ma-136	107	27	q	q	X
ma-136	107	28	]	]	X
ma-136	107	29	(	(	PUNCT
ma-136	107	30	f	f	X
ma-136	107	31	)	)	PUNCT
ma-136	107	32	=	=	SYM
ma-136	108	1	σm,[p	σm,[p	NOUN
ma-136	108	2	,	,	PUNCT
ma-136	108	3	q	q	X
ma-136	108	4	]	]	X
ma-136	108	5	(	(	PUNCT
ma-136	108	6	f	f	X
ma-136	108	7	)	)	PUNCT
ma-136	109	1	=	=	NOUN
ma-136	109	2	∞	∞	NOUN
ma-136	109	3	and	and	CCONJ
ma-136	109	4	σ[p+1,q	σ[p+1,q	NOUN
ma-136	109	5	]	]	PUNCT
ma-136	109	6	(	(	PUNCT
ma-136	109	7	f	f	X
ma-136	109	8	)	)	PUNCT
ma-136	109	9	=	=	SYM
ma-136	110	1	σm,[p+1,q	σm,[p+1,q	X
ma-136	110	2	]	]	PUNCT
ma-136	110	3	(	(	PUNCT
ma-136	110	4	f	f	PROPN
ma-136	110	5	)	)	PUNCT
ma-136	110	6	≥	≥	PROPN
ma-136	110	7	α	α	X
ma-136	110	8	.	.	PUNCT
ma-136	110	9	theorem	theorem	PROPN
ma-136	110	10	b	b	PROPN
ma-136	110	11	(	(	PUNCT
ma-136	110	12	see	see	VERB
ma-136	110	13	[	[	X
ma-136	110	14	5	5	NUM
ma-136	110	15	]	]	PUNCT
ma-136	110	16	)	)	PUNCT
ma-136	110	17	let	let	VERB
ma-136	110	18	p	p	PRON
ma-136	110	19	≥	≥	PRON
ma-136	110	20	q	q	NOUN
ma-136	110	21	≥	≥	NUM
ma-136	110	22	1	1	NUM
ma-136	110	23	be	be	AUX
ma-136	110	24	integers	integer	NOUN
ma-136	110	25	.	.	PUNCT
ma-136	111	1	let	let	VERB
ma-136	111	2	h	h	PRON
ma-136	111	3	be	be	AUX
ma-136	111	4	a	a	DET
ma-136	111	5	set	set	NOUN
ma-136	111	6	of	of	ADP
ma-136	111	7	complex	complex	ADJ
ma-136	111	8	numbers	number	NOUN
ma-136	111	9	satisfying	satisfy	VERB
ma-136	111	10	densd	densd	PROPN
ma-136	111	11	{	{	PUNCT
ma-136	111	12	|z	|z	PROPN
ma-136	112	1	|	|	ADV
ma-136	112	2	:	:	PUNCT
ma-136	112	3	z	z	PROPN
ma-136	112	4	∈	∈	PROPN
ma-136	112	5	h	h	NOUN
ma-136	113	1	⊆	⊆	NUM
ma-136	113	2	d	d	X
ma-136	113	3	}	}	PUNCT
ma-136	113	4	>	>	X
ma-136	113	5	0	0	NUM
ma-136	113	6	,	,	PUNCT
ma-136	113	7	and	and	CCONJ
ma-136	113	8	let	let	VERB
ma-136	113	9	a0	a0	PROPN
ma-136	113	10	(	(	PUNCT
ma-136	113	11	z	z	NOUN
ma-136	113	12	)	)	PUNCT
ma-136	113	13	,	,	PUNCT
ma-136	113	14	...	...	PUNCT
ma-136	113	15	,	,	PUNCT
ma-136	113	16	ak−1	ak−1	INTJ
ma-136	113	17	(	(	PUNCT
ma-136	113	18	z	z	NOUN
ma-136	113	19	)	)	PUNCT
ma-136	113	20	be	be	AUX
ma-136	113	21	analytic	analytic	ADJ
ma-136	113	22	functions	function	NOUN
ma-136	113	23	in	in	ADP
ma-136	113	24	the	the	DET
ma-136	113	25	unit	unit	NOUN
ma-136	113	26	disc	disc	VERB
ma-136	113	27	d	d	PROPN
ma-136	113	28	such	such	ADJ
ma-136	113	29	that	that	PRON
ma-136	113	30	for	for	ADP
ma-136	113	31	real	real	ADJ
ma-136	113	32	constants	constant	NOUN
ma-136	113	33	α	α	NOUN
ma-136	113	34	,	,	PUNCT
ma-136	113	35	β	β	NOUN
ma-136	113	36	,	,	PUNCT
ma-136	113	37	where	where	SCONJ
ma-136	113	38	0	0	NUM
ma-136	113	39	≤	≤	NOUN
ma-136	113	40	β	β	X
ma-136	113	41	<	<	X
ma-136	113	42	α	α	X
ma-136	113	43	,	,	PUNCT
ma-136	113	44	we	we	PRON
ma-136	113	45	have	have	VERB
ma-136	113	46	t	t	NOUN
ma-136	113	47	(	(	PUNCT
ma-136	113	48	r	r	NOUN
ma-136	113	49	,	,	PUNCT
ma-136	113	50	a0	a0	PROPN
ma-136	113	51	)	)	PUNCT
ma-136	113	52	≥	≥	PRON
ma-136	114	1	expp	expp	ADJ
ma-136	114	2	{	{	PUNCT
ma-136	114	3	α	α	PROPN
ma-136	114	4	logq	logq	NOUN
ma-136	114	5	(	(	PUNCT
ma-136	114	6	1	1	NUM
ma-136	114	7	1−	1−	NUM
ma-136	114	8	|z	|z	NOUN
ma-136	114	9	|	|	ADV
ma-136	114	10	)	)	PUNCT
ma-136	114	11	}	}	PUNCT
ma-136	114	12	and	and	CCONJ
ma-136	114	13	t	t	PROPN
ma-136	114	14	(	(	PUNCT
ma-136	114	15	r	r	NOUN
ma-136	114	16	,	,	PUNCT
ma-136	114	17	ai	ai	NOUN
ma-136	114	18	)	)	PUNCT
ma-136	114	19	≤	≤	NUM
ma-136	114	20	expp	expp	ADJ
ma-136	114	21	{	{	PUNCT
ma-136	114	22	β	β	X
ma-136	114	23	logq	logq	NOUN
ma-136	114	24	(	(	PUNCT
ma-136	114	25	1	1	NUM
ma-136	114	26	1−	1−	NUM
ma-136	114	27	|z	|z	NOUN
ma-136	114	28	|	|	ADV
ma-136	114	29	)	)	PUNCT
ma-136	114	30	}	}	PUNCT
ma-136	114	31	(	(	PUNCT
ma-136	114	32	i	i	NOUN
ma-136	114	33	=	=	NOUN
ma-136	114	34	1	1	NUM
ma-136	114	35	,	,	PUNCT
ma-136	114	36	...	...	PUNCT
ma-136	114	37	,	,	PUNCT
ma-136	114	38	k	k	PROPN
ma-136	115	1	−	−	PROPN
ma-136	115	2	1	1	NUM
ma-136	115	3	)	)	PUNCT
ma-136	115	4	as	as	ADP
ma-136	115	5	|z	|z	PROPN
ma-136	115	6	|	|	ADV
ma-136	115	7	=	=	SYM
ma-136	115	8	r	r	NOUN
ma-136	115	9	→	→	SYM
ma-136	115	10	1−	1−	NUM
ma-136	115	11	for	for	ADP
ma-136	115	12	z	z	PROPN
ma-136	115	13	∈	∈	PROPN
ma-136	115	14	h.	h.	NOUN
ma-136	115	15	then	then	ADV
ma-136	115	16	every	every	DET
ma-136	115	17	solution	solution	NOUN
ma-136	115	18	f	f	PROPN
ma-136	115	19	6≡	6≡	NUM
ma-136	115	20	0	0	NUM
ma-136	115	21	of	of	ADP
ma-136	115	22	equation	equation	NOUN
ma-136	115	23	(	(	PUNCT
ma-136	115	24	1.1	1.1	NUM
ma-136	115	25	)	)	PUNCT
ma-136	115	26	satisfies	satisfy	VERB
ma-136	115	27	σ[p	σ[p	NOUN
ma-136	115	28	,	,	PUNCT
ma-136	115	29	q	q	X
ma-136	115	30	]	]	X
ma-136	115	31	(	(	PUNCT
ma-136	115	32	f	f	X
ma-136	115	33	)	)	PUNCT
ma-136	115	34	=	=	SYM
ma-136	116	1	σm,[p	σm,[p	NOUN
ma-136	116	2	,	,	PUNCT
ma-136	116	3	q	q	X
ma-136	116	4	]	]	X
ma-136	116	5	(	(	PUNCT
ma-136	116	6	f	f	X
ma-136	116	7	)	)	PUNCT
ma-136	117	1	=	=	NOUN
ma-136	117	2	∞	∞	NOUN
ma-136	117	3	and	and	CCONJ
ma-136	117	4	σ[p+1,q	σ[p+1,q	NOUN
ma-136	117	5	]	]	PUNCT
ma-136	117	6	(	(	PUNCT
ma-136	117	7	f	f	X
ma-136	117	8	)	)	PUNCT
ma-136	117	9	=	=	SYM
ma-136	118	1	σm,[p+1,q	σm,[p+1,q	X
ma-136	118	2	]	]	PUNCT
ma-136	118	3	(	(	PUNCT
ma-136	118	4	f	f	PROPN
ma-136	118	5	)	)	PUNCT
ma-136	118	6	≥	≥	PROPN
ma-136	118	7	α	α	X
ma-136	118	8	.	.	PUNCT
ma-136	119	1	https://doi.org/10.28924/ada/ma.3.10	https://doi.org/10.28924/ada/ma.3.10	PROPN
ma-136	119	2	eur	eur	PROPN
ma-136	119	3	.	.	PUNCT
ma-136	120	1	j.	j.	PROPN
ma-136	120	2	math	math	PROPN
ma-136	120	3	.	.	PUNCT
ma-136	121	1	anal	anal	PROPN
ma-136	121	2	.	.	PUNCT
ma-136	122	1	10.28924	10.28924	NUM
ma-136	122	2	/	/	SYM
ma-136	122	3	ada	ada	NOUN
ma-136	122	4	/	/	NOUN
ma-136	122	5	ma.3.10	ma.3.10	NOUN
ma-136	122	6	5after	5after	NUM
ma-136	122	7	that	that	PRON
ma-136	122	8	in	in	ADP
ma-136	122	9	2021	2021	NUM
ma-136	122	10	,	,	PUNCT
ma-136	122	11	chen	chen	PROPN
ma-136	122	12	et	et	PROPN
ma-136	122	13	al	al	PROPN
ma-136	122	14	.	.	PUNCT
ma-136	123	1	[	[	X
ma-136	123	2	9	9	NUM
ma-136	123	3	]	]	PUNCT
ma-136	123	4	investigated	investigate	VERB
ma-136	123	5	the	the	DET
ma-136	123	6	growth	growth	NOUN
ma-136	123	7	of	of	ADP
ma-136	123	8	solutions	solution	NOUN
ma-136	123	9	of	of	ADP
ma-136	123	10	equations	equation	NOUN
ma-136	123	11	(	(	PUNCT
ma-136	123	12	1.1	1.1	NUM
ma-136	123	13	)	)	PUNCT
ma-136	123	14	and	and	CCONJ
ma-136	123	15	(	(	PUNCT
ma-136	123	16	1.2	1.2	NUM
ma-136	123	17	)	)	PUNCT
ma-136	123	18	in	in	ADP
ma-136	123	19	d	d	PROPN
ma-136	123	20	by	by	ADP
ma-136	123	21	using	use	VERB
ma-136	123	22	the	the	DET
ma-136	123	23	iterated	iterated	ADJ
ma-136	123	24	order	order	NOUN
ma-136	123	25	,	,	PUNCT
ma-136	123	26	and	and	CCONJ
ma-136	123	27	they	they	PRON
ma-136	123	28	got	get	VERB
ma-136	123	29	the	the	DET
ma-136	123	30	following	follow	VERB
ma-136	123	31	results	result	NOUN
ma-136	123	32	.	.	PUNCT
ma-136	124	1	theorem	theorem	PROPN
ma-136	124	2	c	c	PROPN
ma-136	124	3	(	(	PUNCT
ma-136	124	4	see	see	VERB
ma-136	124	5	[	[	X
ma-136	124	6	9	9	NUM
ma-136	124	7	]	]	PUNCT
ma-136	124	8	)	)	PUNCT
ma-136	124	9	let	let	VERB
ma-136	124	10	n	n	PRON
ma-136	124	11	≥	≥	X
ma-136	124	12	1	1	NUM
ma-136	124	13	be	be	AUX
ma-136	124	14	an	an	DET
ma-136	124	15	integer	integer	NOUN
ma-136	124	16	.	.	PUNCT
ma-136	125	1	let	let	VERB
ma-136	125	2	h	h	PRON
ma-136	125	3	be	be	AUX
ma-136	125	4	a	a	DET
ma-136	125	5	set	set	NOUN
ma-136	125	6	of	of	ADP
ma-136	125	7	complex	complex	ADJ
ma-136	125	8	numbers	number	NOUN
ma-136	125	9	satisfying	satisfy	VERB
ma-136	125	10	densd	densd	PROPN
ma-136	125	11	{	{	PUNCT
ma-136	125	12	|z	|z	PROPN
ma-136	126	1	|	|	ADV
ma-136	126	2	:	:	PUNCT
ma-136	126	3	z	z	PROPN
ma-136	126	4	∈	∈	PROPN
ma-136	126	5	h	h	NOUN
ma-136	127	1	⊆	⊆	NUM
ma-136	127	2	d	d	X
ma-136	127	3	}	}	PUNCT
ma-136	127	4	>	>	X
ma-136	127	5	0	0	NUM
ma-136	127	6	,	,	PUNCT
ma-136	127	7	and	and	CCONJ
ma-136	127	8	let	let	VERB
ma-136	127	9	a0	a0	PROPN
ma-136	127	10	,	,	PUNCT
ma-136	127	11	a1	a1	PROPN
ma-136	127	12	,	,	PUNCT
ma-136	127	13	...	...	PUNCT
ma-136	127	14	,	,	PUNCT
ma-136	127	15	ak−1	ak−1	ADV
ma-136	127	16	be	be	AUX
ma-136	127	17	analytic	analytic	ADJ
ma-136	127	18	functions	function	NOUN
ma-136	127	19	in	in	ADP
ma-136	127	20	the	the	DET
ma-136	127	21	unit	unit	NOUN
ma-136	127	22	disc	disc	VERB
ma-136	127	23	d	d	PROPN
ma-136	127	24	such	such	ADJ
ma-136	127	25	that	that	DET
ma-136	127	26	max	max	PROPN
ma-136	127	27	{	{	PUNCT
ma-136	127	28	σm	σm	PROPN
ma-136	127	29	,	,	PUNCT
ma-136	127	30	n	n	CCONJ
ma-136	127	31	(	(	PUNCT
ma-136	127	32	ai	ai	PROPN
ma-136	127	33	)	)	PUNCT
ma-136	127	34	:	:	PUNCT
ma-136	128	1	i	i	NOUN
ma-136	128	2	=	=	NOUN
ma-136	128	3	1	1	NUM
ma-136	128	4	,	,	PUNCT
ma-136	128	5	2	2	NUM
ma-136	128	6	,	,	PUNCT
ma-136	128	7	...	...	PUNCT
ma-136	128	8	,	,	PUNCT
ma-136	128	9	k	k	PROPN
ma-136	129	1	−	−	PROPN
ma-136	129	2	1	1	NUM
ma-136	129	3	}	}	PUNCT
ma-136	129	4	≤	≤	NUM
ma-136	129	5	σm	σm	NOUN
ma-136	129	6	,	,	PUNCT
ma-136	129	7	n	n	PROPN
ma-136	129	8	(	(	PUNCT
ma-136	129	9	a0	a0	PROPN
ma-136	129	10	)	)	PUNCT
ma-136	129	11	=	=	SYM
ma-136	129	12	µ	µ	X
ma-136	129	13	(	(	PUNCT
ma-136	129	14	0	0	NUM
ma-136	129	15	<	<	X
ma-136	129	16	µ	µ	X
ma-136	129	17	<	<	X
ma-136	129	18	∞	∞	NUM
ma-136	129	19	)	)	PUNCT
ma-136	129	20	,	,	PUNCT
ma-136	129	21	and	and	CCONJ
ma-136	129	22	for	for	ADP
ma-136	129	23	a	a	DET
ma-136	129	24	constant	constant	ADJ
ma-136	129	25	α	α	PRON
ma-136	129	26	≥	≥	NOUN
ma-136	129	27	0	0	NUM
ma-136	129	28	,	,	PUNCT
ma-136	129	29	we	we	PRON
ma-136	129	30	have	have	VERB
ma-136	129	31	lim	lim	PROPN
ma-136	129	32	inf	inf	PROPN
ma-136	129	33	|z	|z	PROPN
ma-136	129	34	|→1−,z∈h	|→1−,z∈h	PROPN
ma-136	129	35	(	(	PUNCT
ma-136	129	36	(	(	PUNCT
ma-136	129	37	1−	1−	NUM
ma-136	129	38	|z	|z	PROPN
ma-136	129	39	|)µ	|)µ	PROPN
ma-136	129	40	logn	logn	VERB
ma-136	129	41	|a0	|a0	PROPN
ma-136	129	42	(	(	PUNCT
ma-136	129	43	z)|	z)|	INTJ
ma-136	129	44	)	)	PUNCT
ma-136	129	45	>	>	X
ma-136	129	46	α	α	PROPN
ma-136	129	47	and	and	CCONJ
ma-136	129	48	|ai	|ai	NUM
ma-136	129	49	(	(	PUNCT
ma-136	129	50	z)|	z)|	ADP
ma-136	129	51	≤	≤	PROPN
ma-136	129	52	expn	expn	ADJ
ma-136	129	53	{	{	PUNCT
ma-136	129	54	α	α	PROPN
ma-136	129	55	(	(	PUNCT
ma-136	129	56	1	1	NUM
ma-136	129	57	1−	1−	NUM
ma-136	129	58	|z	|z	PROPN
ma-136	129	59	|	|	ADV
ma-136	129	60	)	)	PUNCT
ma-136	129	61	µ	µ	NOUN
ma-136	129	62	}	}	PUNCT
ma-136	129	63	,	,	PUNCT
ma-136	129	64	(	(	PUNCT
ma-136	129	65	i	i	NOUN
ma-136	129	66	=	=	NOUN
ma-136	129	67	1	1	NUM
ma-136	129	68	,	,	PUNCT
ma-136	129	69	2	2	NUM
ma-136	129	70	,	,	PUNCT
ma-136	129	71	...	...	PUNCT
ma-136	129	72	,	,	PUNCT
ma-136	129	73	k	k	PROPN
ma-136	129	74	−	−	PROPN
ma-136	129	75	1	1	NUM
ma-136	129	76	)	)	PUNCT
ma-136	129	77	as	as	ADP
ma-136	129	78	|z	|z	PROPN
ma-136	129	79	|	|	PROPN
ma-136	129	80	→	→	SYM
ma-136	129	81	1−	1−	NUM
ma-136	129	82	for	for	ADP
ma-136	129	83	z	z	PROPN
ma-136	129	84	∈	∈	PROPN
ma-136	129	85	h.	h.	NOUN
ma-136	129	86	then	then	ADV
ma-136	129	87	every	every	DET
ma-136	129	88	solution	solution	NOUN
ma-136	129	89	f	f	PROPN
ma-136	129	90	6≡	6≡	NUM
ma-136	129	91	0	0	NUM
ma-136	129	92	of	of	ADP
ma-136	129	93	equation	equation	NOUN
ma-136	129	94	(	(	PUNCT
ma-136	129	95	1.1	1.1	NUM
ma-136	129	96	)	)	PUNCT
ma-136	129	97	satisfies	satisfy	VERB
ma-136	129	98	σn	σn	X
ma-136	129	99	(	(	PUNCT
ma-136	129	100	f	f	PROPN
ma-136	129	101	)	)	PUNCT
ma-136	130	1	=	=	SYM
ma-136	130	2	σm	σm	NOUN
ma-136	130	3	,	,	PUNCT
ma-136	130	4	n	n	PROPN
ma-136	130	5	(	(	PUNCT
ma-136	130	6	f	f	NOUN
ma-136	130	7	)	)	PUNCT
ma-136	131	1	=	=	SYM
ma-136	131	2	∞	∞	PROPN
ma-136	131	3	and	and	CCONJ
ma-136	131	4	σn+1	σn+1	PROPN
ma-136	131	5	(	(	PUNCT
ma-136	131	6	f	f	PROPN
ma-136	131	7	)	)	PUNCT
ma-136	131	8	=	=	SYM
ma-136	131	9	σm	σm	NOUN
ma-136	131	10	,	,	PUNCT
ma-136	131	11	n	n	PROPN
ma-136	131	12	(	(	PUNCT
ma-136	131	13	a0	a0	PROPN
ma-136	131	14	)	)	PUNCT
ma-136	132	1	=	=	SYM
ma-136	132	2	µ.	µ.	PROPN
ma-136	132	3	theorem	theorem	ADJ
ma-136	132	4	d	d	X
ma-136	132	5	(	(	PUNCT
ma-136	132	6	see	see	VERB
ma-136	132	7	[	[	X
ma-136	132	8	9	9	NUM
ma-136	132	9	]	]	PUNCT
ma-136	132	10	)	)	PUNCT
ma-136	132	11	let	let	VERB
ma-136	132	12	n	n	PRON
ma-136	132	13	≥	≥	X
ma-136	132	14	1	1	NUM
ma-136	132	15	be	be	AUX
ma-136	132	16	an	an	DET
ma-136	132	17	integer	integer	NOUN
ma-136	132	18	.	.	PUNCT
ma-136	133	1	let	let	VERB
ma-136	133	2	h	h	PRON
ma-136	133	3	be	be	AUX
ma-136	133	4	a	a	DET
ma-136	133	5	set	set	NOUN
ma-136	133	6	of	of	ADP
ma-136	133	7	complex	complex	ADJ
ma-136	133	8	numbers	number	NOUN
ma-136	133	9	satisfying	satisfy	VERB
ma-136	133	10	densd	densd	PROPN
ma-136	133	11	{	{	PUNCT
ma-136	133	12	|z	|z	PROPN
ma-136	134	1	|	|	ADV
ma-136	134	2	:	:	PUNCT
ma-136	134	3	z	z	PROPN
ma-136	134	4	∈	∈	PROPN
ma-136	134	5	h	h	NOUN
ma-136	135	1	⊆	⊆	NUM
ma-136	135	2	d	d	X
ma-136	135	3	}	}	PUNCT
ma-136	135	4	>	>	X
ma-136	135	5	0	0	NUM
ma-136	135	6	,	,	PUNCT
ma-136	135	7	and	and	CCONJ
ma-136	135	8	let	let	VERB
ma-136	135	9	a0	a0	PROPN
ma-136	135	10	,	,	PUNCT
ma-136	135	11	a1	a1	PROPN
ma-136	135	12	,	,	PUNCT
ma-136	135	13	...	...	PUNCT
ma-136	135	14	,	,	PUNCT
ma-136	135	15	ak	ak	PROPN
ma-136	135	16	be	be	AUX
ma-136	135	17	analytic	analytic	ADJ
ma-136	135	18	functions	function	NOUN
ma-136	135	19	in	in	ADP
ma-136	135	20	the	the	DET
ma-136	135	21	unit	unit	NOUN
ma-136	135	22	disc	disc	VERB
ma-136	135	23	d	d	PROPN
ma-136	135	24	,	,	PUNCT
ma-136	135	25	and	and	CCONJ
ma-136	135	26	for	for	ADP
ma-136	135	27	some	some	DET
ma-136	135	28	constants	constant	NOUN
ma-136	135	29	α	α	DET
ma-136	135	30	≥	≥	NOUN
ma-136	135	31	0	0	NUM
ma-136	135	32	and	and	CCONJ
ma-136	135	33	µ	µ	X
ma-136	135	34	>	>	X
ma-136	135	35	0	0	NUM
ma-136	135	36	,	,	PUNCT
ma-136	135	37	we	we	PRON
ma-136	135	38	have	have	VERB
ma-136	135	39	lim	lim	PROPN
ma-136	135	40	inf	inf	PROPN
ma-136	135	41	|z	|z	PROPN
ma-136	135	42	|→1−,z∈h	|→1−,z∈h	PROPN
ma-136	135	43	(	(	PUNCT
ma-136	135	44	(	(	PUNCT
ma-136	135	45	1−	1−	NUM
ma-136	135	46	|z	|z	PROPN
ma-136	135	47	|)µ	|)µ	PROPN
ma-136	135	48	logn−1	logn−1	PROPN
ma-136	135	49	t	t	PROPN
ma-136	135	50	(	(	PUNCT
ma-136	135	51	r	r	NOUN
ma-136	135	52	,	,	PUNCT
ma-136	135	53	a0	a0	NOUN
ma-136	135	54	)	)	PUNCT
ma-136	135	55	)	)	PUNCT
ma-136	135	56	>	>	X
ma-136	136	1	α	α	PROPN
ma-136	136	2	and	and	CCONJ
ma-136	136	3	t	t	PROPN
ma-136	136	4	(	(	PUNCT
ma-136	136	5	r	r	NOUN
ma-136	136	6	,	,	PUNCT
ma-136	136	7	ai	ai	NOUN
ma-136	136	8	)	)	PUNCT
ma-136	136	9	≤	≤	NOUN
ma-136	136	10	expn−1	expn−1	NOUN
ma-136	136	11	{	{	PUNCT
ma-136	136	12	α	α	PROPN
ma-136	136	13	(	(	PUNCT
ma-136	136	14	1	1	NUM
ma-136	136	15	1−	1−	NUM
ma-136	136	16	|z	|z	PROPN
ma-136	137	1	|	|	ADV
ma-136	137	2	)	)	PUNCT
ma-136	137	3	µ	µ	NOUN
ma-136	137	4	}	}	PUNCT
ma-136	137	5	,	,	PUNCT
ma-136	137	6	(	(	PUNCT
ma-136	137	7	i	i	NOUN
ma-136	137	8	=	=	NOUN
ma-136	137	9	1	1	NUM
ma-136	137	10	,	,	PUNCT
ma-136	137	11	2	2	NUM
ma-136	137	12	,	,	PUNCT
ma-136	137	13	...	...	PUNCT
ma-136	137	14	,	,	PUNCT
ma-136	137	15	k	k	NOUN
ma-136	137	16	)	)	PUNCT
ma-136	137	17	as	as	ADP
ma-136	137	18	|z	|z	PROPN
ma-136	137	19	|	|	ADV
ma-136	137	20	=	=	SYM
ma-136	137	21	r	r	NOUN
ma-136	137	22	→	→	SYM
ma-136	137	23	1−	1−	NUM
ma-136	137	24	for	for	ADP
ma-136	137	25	z	z	PROPN
ma-136	137	26	∈	∈	PROPN
ma-136	137	27	h.	h.	NOUN
ma-136	137	28	then	then	ADV
ma-136	137	29	every	every	DET
ma-136	137	30	meromorphic	meromorphic	ADJ
ma-136	137	31	(	(	PUNCT
ma-136	137	32	or	or	CCONJ
ma-136	137	33	analytic	analytic	ADJ
ma-136	137	34	)	)	PUNCT
ma-136	137	35	solution	solution	NOUN
ma-136	137	36	f	f	PROPN
ma-136	137	37	6≡	6≡	NUM
ma-136	137	38	0	0	NUM
ma-136	137	39	of	of	ADP
ma-136	137	40	equation	equation	NOUN
ma-136	137	41	(	(	PUNCT
ma-136	137	42	1.2	1.2	NUM
ma-136	137	43	)	)	PUNCT
ma-136	137	44	satisfies	satisfy	VERB
ma-136	137	45	σn	σn	X
ma-136	137	46	(	(	PUNCT
ma-136	137	47	f	f	NOUN
ma-136	137	48	)	)	PUNCT
ma-136	138	1	=	=	NOUN
ma-136	138	2	∞	∞	NUM
ma-136	138	3	and	and	CCONJ
ma-136	138	4	σn+1	σn+1	PROPN
ma-136	138	5	(	(	PUNCT
ma-136	138	6	f	f	PROPN
ma-136	138	7	)	)	PUNCT
ma-136	138	8	≥	≥	PROPN
ma-136	138	9	µ.	µ.	PROPN
ma-136	138	10	theorem	theorem	PROPN
ma-136	138	11	e	e	PROPN
ma-136	138	12	(	(	PUNCT
ma-136	138	13	see	see	VERB
ma-136	138	14	[	[	X
ma-136	138	15	9	9	NUM
ma-136	138	16	]	]	PUNCT
ma-136	138	17	)	)	PUNCT
ma-136	138	18	assume	assume	VERB
ma-136	138	19	that	that	SCONJ
ma-136	138	20	the	the	DET
ma-136	138	21	assumptions	assumption	NOUN
ma-136	138	22	of	of	ADP
ma-136	138	23	theorem	theorem	NOUN
ma-136	138	24	c	c	PROPN
ma-136	138	25	hold	hold	NOUN
ma-136	138	26	.	.	PUNCT
ma-136	139	1	then	then	ADV
ma-136	139	2	every	every	DET
ma-136	139	3	solution	solution	NOUN
ma-136	139	4	f	f	PROPN
ma-136	139	5	6≡	6≡	NUM
ma-136	139	6	0	0	NUM
ma-136	139	7	of	of	ADP
ma-136	139	8	equation	equation	NOUN
ma-136	139	9	(	(	PUNCT
ma-136	139	10	1.1	1.1	NUM
ma-136	139	11	)	)	PUNCT
ma-136	139	12	satisfies	satisfy	VERB
ma-136	139	13	λ̄n	λ̄n	PROPN
ma-136	139	14	(	(	PUNCT
ma-136	139	15	f	f	PROPN
ma-136	139	16	(	(	PUNCT
ma-136	139	17	j	j	PROPN
ma-136	139	18	)	)	PUNCT
ma-136	139	19	−	−	PROPN
ma-136	139	20	z	z	NOUN
ma-136	139	21	)	)	PUNCT
ma-136	140	1	=	=	SYM
ma-136	140	2	λ̄n	λ̄n	PROPN
ma-136	140	3	(	(	PUNCT
ma-136	140	4	f	f	PROPN
ma-136	140	5	−	−	PROPN
ma-136	140	6	z	z	PROPN
ma-136	140	7	)	)	PUNCT
ma-136	140	8	=	=	NOUN
ma-136	140	9	σn	σn	X
ma-136	140	10	(	(	PUNCT
ma-136	140	11	f	f	NOUN
ma-136	140	12	)	)	PUNCT
ma-136	141	1	=	=	SYM
ma-136	141	2	∞	∞	PROPN
ma-136	141	3	,	,	PUNCT
ma-136	141	4	λ̄n+1	λ̄n+1	PROPN
ma-136	141	5	(	(	PUNCT
ma-136	141	6	f	f	PROPN
ma-136	141	7	(	(	PUNCT
ma-136	141	8	j	j	PROPN
ma-136	141	9	)	)	PUNCT
ma-136	141	10	−	−	PROPN
ma-136	141	11	z	z	NOUN
ma-136	141	12	)	)	PUNCT
ma-136	142	1	=	=	SYM
ma-136	142	2	λ̄n+1	λ̄n+1	NOUN
ma-136	142	3	(	(	PUNCT
ma-136	142	4	f	f	PROPN
ma-136	142	5	−	−	PROPN
ma-136	142	6	z	z	PROPN
ma-136	142	7	)	)	PUNCT
ma-136	142	8	=	=	SYM
ma-136	142	9	σn+1	σn+1	PROPN
ma-136	142	10	(	(	PUNCT
ma-136	142	11	f	f	PROPN
ma-136	142	12	)	)	PUNCT
ma-136	142	13	=	=	SYM
ma-136	142	14	µ	µ	X
ma-136	142	15	,	,	PUNCT
ma-136	142	16	(	(	PUNCT
ma-136	142	17	j	j	NOUN
ma-136	142	18	=	=	SYM
ma-136	142	19	1	1	NUM
ma-136	142	20	,	,	PUNCT
ma-136	142	21	2	2	NUM
ma-136	142	22	,	,	PUNCT
ma-136	142	23	...	...	PUNCT
ma-136	142	24	)	)	PUNCT
ma-136	142	25	.in	.in	PUNCT
ma-136	143	1	this	this	DET
ma-136	143	2	paper	paper	NOUN
ma-136	143	3	,	,	PUNCT
ma-136	143	4	we	we	PRON
ma-136	143	5	improve	improve	VERB
ma-136	143	6	and	and	CCONJ
ma-136	143	7	generalize	generalize	VERB
ma-136	143	8	the	the	DET
ma-136	143	9	recent	recent	ADJ
ma-136	143	10	results	result	NOUN
ma-136	143	11	of	of	ADP
ma-136	143	12	chen	chen	PROPN
ma-136	143	13	et	et	PROPN
ma-136	143	14	al	al	PROPN
ma-136	143	15	.	.	PUNCT
ma-136	144	1	[	[	X
ma-136	144	2	9	9	NUM
ma-136	144	3	]	]	PUNCT
ma-136	144	4	by	by	ADP
ma-136	144	5	using	use	VERB
ma-136	144	6	theconcept	theconcept	NOUN
ma-136	144	7	of	of	ADP
ma-136	144	8	[	[	X
ma-136	144	9	p	p	X
ma-136	144	10	,	,	PUNCT
ma-136	144	11	q]−order	q]−order	NOUN
ma-136	144	12	instead	instead	ADV
ma-136	144	13	of	of	ADP
ma-136	144	14	the	the	DET
ma-136	144	15	iterated	iterated	ADJ
ma-136	144	16	order	order	NOUN
ma-136	144	17	with	with	ADP
ma-136	144	18	less	less	ADJ
ma-136	144	19	control	control	NOUN
ma-136	144	20	constant	constant	ADJ
ma-136	144	21	.	.	PUNCT
ma-136	145	1	at	at	ADP
ma-136	145	2	the	the	DET
ma-136	145	3	same	same	ADJ
ma-136	145	4	time	time	NOUN
ma-136	145	5	,	,	PUNCT
ma-136	145	6	our	our	PRON
ma-136	145	7	work	work	NOUN
ma-136	145	8	improve	improve	VERB
ma-136	145	9	some	some	DET
ma-136	145	10	results	result	NOUN
ma-136	145	11	of	of	ADP
ma-136	145	12	belaïdi	belaïdi	NOUN
ma-136	145	13	in	in	ADP
ma-136	145	14	[	[	X
ma-136	145	15	4	4	NUM
ma-136	145	16	]	]	PUNCT
ma-136	145	17	and	and	CCONJ
ma-136	145	18	[	[	X
ma-136	145	19	5	5	NUM
ma-136	145	20	]	]	PUNCT
ma-136	145	21	.	.	PUNCT
ma-136	146	1	to	to	PART
ma-136	146	2	be	be	AUX
ma-136	146	3	specific	specific	ADJ
ma-136	146	4	,	,	PUNCT
ma-136	146	5	we	we	PRON
ma-136	146	6	will	will	AUX
ma-136	146	7	decrease	decrease	VERB
ma-136	146	8	the	the	DET
ma-136	146	9	controlconstants	controlconstant	NOUN
ma-136	146	10	of	of	ADP
ma-136	146	11	the	the	DET
ma-136	146	12	coefficients	coefficient	NOUN
ma-136	146	13	’	'	PUNCT
ma-136	146	14	modulus	modulus	ADJ
ma-136	146	15	or	or	CCONJ
ma-136	146	16	characteristic	characteristic	ADJ
ma-136	146	17	functions	function	NOUN
ma-136	146	18	and	and	CCONJ
ma-136	146	19	obtain	obtain	VERB
ma-136	146	20	the	the	DET
ma-136	146	21	same	same	ADJ
ma-136	146	22	results	result	NOUN
ma-136	146	23	ofbelaïdi	ofbelaïdi	NOUN
ma-136	146	24	,	,	PUNCT
ma-136	146	25	tu	tu	PROPN
ma-136	146	26	and	and	CCONJ
ma-136	146	27	xuan	xuan	PROPN
ma-136	146	28	.	.	PUNCT
ma-136	147	1	here	here	ADV
ma-136	147	2	,	,	PUNCT
ma-136	147	3	we	we	PRON
ma-136	147	4	study	study	VERB
ma-136	147	5	the	the	DET
ma-136	147	6	problem	problem	NOUN
ma-136	147	7	and	and	CCONJ
ma-136	147	8	get	get	VERB
ma-136	147	9	the	the	DET
ma-136	147	10	following	follow	VERB
ma-136	147	11	results	result	NOUN
ma-136	147	12	.	.	PUNCT
ma-136	148	1	https://doi.org/10.28924/ada/ma.3.10	https://doi.org/10.28924/ada/ma.3.10	ADV
ma-136	148	2	eur	eur	PROPN
ma-136	148	3	.	.	PUNCT
ma-136	149	1	j.	j.	PROPN
ma-136	149	2	math	math	PROPN
ma-136	149	3	.	.	PUNCT
ma-136	150	1	anal	anal	PROPN
ma-136	150	2	.	.	PUNCT
ma-136	151	1	10.28924	10.28924	NUM
ma-136	151	2	/	/	SYM
ma-136	151	3	ada	ada	NOUN
ma-136	151	4	/	/	SYM
ma-136	151	5	ma.3.10	ma.3.10	ADJ
ma-136	151	6	6	6	NUM
ma-136	151	7	theorem	theorem	NOUN
ma-136	151	8	1.1	1.1	NUM
ma-136	151	9	let	let	VERB
ma-136	151	10	p	p	PRON
ma-136	151	11	≥	≥	PRON
ma-136	151	12	q	q	NOUN
ma-136	151	13	≥	≥	NUM
ma-136	151	14	1	1	NUM
ma-136	151	15	be	be	AUX
ma-136	151	16	integers	integer	NOUN
ma-136	151	17	.	.	PUNCT
ma-136	152	1	let	let	VERB
ma-136	152	2	h	h	PRON
ma-136	152	3	be	be	AUX
ma-136	152	4	a	a	DET
ma-136	152	5	set	set	NOUN
ma-136	152	6	of	of	ADP
ma-136	152	7	complex	complex	ADJ
ma-136	152	8	numbers	number	NOUN
ma-136	152	9	satisfying	satisfy	VERB
ma-136	152	10	densd	densd	PROPN
ma-136	152	11	{	{	PUNCT
ma-136	152	12	|z	|z	PROPN
ma-136	153	1	|	|	ADV
ma-136	153	2	:	:	PUNCT
ma-136	153	3	z	z	PROPN
ma-136	153	4	∈	∈	PROPN
ma-136	153	5	h	h	NOUN
ma-136	154	1	⊆	⊆	NUM
ma-136	154	2	d	d	X
ma-136	154	3	}	}	PUNCT
ma-136	154	4	>	>	X
ma-136	154	5	0	0	NUM
ma-136	154	6	,	,	PUNCT
ma-136	154	7	and	and	CCONJ
ma-136	154	8	let	let	VERB
ma-136	154	9	a0	a0	PROPN
ma-136	154	10	,	,	PUNCT
ma-136	154	11	...	...	PUNCT
ma-136	154	12	,	,	PUNCT
ma-136	154	13	ak−1	ak−1	ADV
ma-136	154	14	be	be	AUX
ma-136	154	15	analytic	analytic	ADJ
ma-136	154	16	functions	function	NOUN
ma-136	154	17	in	in	ADP
ma-136	154	18	the	the	DET
ma-136	154	19	unit	unit	NOUN
ma-136	154	20	disc	disc	VERB
ma-136	154	21	d	d	PROPN
ma-136	154	22	such	such	ADJ
ma-136	154	23	that	that	DET
ma-136	154	24	max	max	PROPN
ma-136	154	25	{	{	PUNCT
ma-136	154	26	σm,[p	σm,[p	PROPN
ma-136	154	27	,	,	PUNCT
ma-136	154	28	q	q	X
ma-136	154	29	]	]	X
ma-136	154	30	(	(	PUNCT
ma-136	154	31	ai	ai	PROPN
ma-136	154	32	)	)	PUNCT
ma-136	154	33	:	:	PUNCT
ma-136	155	1	i	i	NOUN
ma-136	155	2	=	=	NOUN
ma-136	155	3	1	1	NUM
ma-136	155	4	,	,	PUNCT
ma-136	155	5	2	2	NUM
ma-136	155	6	,	,	PUNCT
ma-136	155	7	...	...	PUNCT
ma-136	155	8	,	,	PUNCT
ma-136	155	9	k	k	PROPN
ma-136	155	10	−	−	PROPN
ma-136	155	11	1	1	NUM
ma-136	155	12	}	}	PUNCT
ma-136	155	13	≤	≤	NUM
ma-136	155	14	σm,[p	σm,[p	NOUN
ma-136	155	15	,	,	PUNCT
ma-136	155	16	q	q	X
ma-136	155	17	]	]	X
ma-136	155	18	(	(	PUNCT
ma-136	155	19	a0	a0	PROPN
ma-136	155	20	)	)	PUNCT
ma-136	155	21	=	=	SYM
ma-136	155	22	µ	µ	X
ma-136	155	23	(	(	PUNCT
ma-136	155	24	0	0	NUM
ma-136	155	25	<	<	X
ma-136	155	26	µ	µ	X
ma-136	155	27	<	<	X
ma-136	155	28	+	+	NOUN
ma-136	155	29	∞	∞	NOUN
ma-136	155	30	)	)	PUNCT
ma-136	155	31	and	and	CCONJ
ma-136	155	32	for	for	ADP
ma-136	155	33	a	a	DET
ma-136	155	34	constant	constant	ADJ
ma-136	155	35	α	α	PRON
ma-136	155	36	≥	≥	NOUN
ma-136	155	37	0	0	NUM
ma-136	155	38	,	,	PUNCT
ma-136	155	39	we	we	PRON
ma-136	155	40	have	have	VERB
ma-136	155	41	lim	lim	PROPN
ma-136	155	42	inf	inf	PROPN
ma-136	155	43	|z	|z	PROPN
ma-136	155	44	|→1−,z∈h	|→1−,z∈h	PROPN
ma-136	155	45	logp	logp	NOUN
ma-136	155	46	|a0	|a0	PROPN
ma-136	155	47	(	(	PUNCT
ma-136	155	48	z)|	z)|	X
ma-136	155	49	(	(	PUNCT
ma-136	155	50	logq−1	logq−1	X
ma-136	155	51	(	(	PUNCT
ma-136	155	52	1	1	NUM
ma-136	155	53	1−|z	1−|z	NUM
ma-136	155	54	|	|	NOUN
ma-136	155	55	)	)	PUNCT
ma-136	155	56	)	)	PUNCT
ma-136	155	57	µ	µ	X
ma-136	155	58	>	>	X
ma-136	155	59	α	α	PROPN
ma-136	155	60	(	(	PUNCT
ma-136	155	61	1.3	1.3	NUM
ma-136	155	62	)	)	PUNCT
ma-136	155	63	and	and	CCONJ
ma-136	155	64	|ai	|ai	NUM
ma-136	155	65	(	(	PUNCT
ma-136	155	66	z)|	z)|	ADP
ma-136	155	67	≤	≤	NUM
ma-136	155	68	expp	expp	ADJ
ma-136	155	69	{	{	PUNCT
ma-136	155	70	α	α	PROPN
ma-136	155	71	(	(	PUNCT
ma-136	155	72	logq−1	logq−1	X
ma-136	155	73	(	(	PUNCT
ma-136	155	74	1	1	NUM
ma-136	155	75	1−|z	1−|z	NUM
ma-136	155	76	|	|	NOUN
ma-136	155	77	)	)	PUNCT
ma-136	155	78	)	)	PUNCT
ma-136	155	79	µ	µ	X
ma-136	155	80	}	}	PUNCT
ma-136	155	81	(	(	PUNCT
ma-136	155	82	i	i	NOUN
ma-136	155	83	=	=	NOUN
ma-136	155	84	1	1	NUM
ma-136	155	85	,	,	PUNCT
ma-136	155	86	...	...	PUNCT
ma-136	155	87	,	,	PUNCT
ma-136	155	88	k	k	PROPN
ma-136	155	89	−	−	PROPN
ma-136	155	90	1	1	NUM
ma-136	155	91	)	)	PUNCT
ma-136	155	92	(	(	PUNCT
ma-136	155	93	1.4	1.4	NUM
ma-136	155	94	)	)	PUNCT
ma-136	155	95	as	as	ADP
ma-136	155	96	|z	|z	PROPN
ma-136	155	97	|	|	PROPN
ma-136	155	98	→	→	SYM
ma-136	155	99	1−	1−	NUM
ma-136	155	100	for	for	ADP
ma-136	155	101	z	z	PROPN
ma-136	155	102	∈	∈	PROPN
ma-136	155	103	h.	h.	NOUN
ma-136	155	104	then	then	ADV
ma-136	155	105	every	every	DET
ma-136	155	106	solution	solution	NOUN
ma-136	155	107	f	f	PROPN
ma-136	155	108	6≡	6≡	NUM
ma-136	155	109	0	0	NUM
ma-136	155	110	of	of	ADP
ma-136	155	111	equation	equation	NOUN
ma-136	155	112	(	(	PUNCT
ma-136	155	113	1.1	1.1	NUM
ma-136	155	114	)	)	PUNCT
ma-136	155	115	satisfies	satisfy	VERB
ma-136	155	116	σ[p	σ[p	NOUN
ma-136	155	117	,	,	PUNCT
ma-136	155	118	q	q	X
ma-136	155	119	]	]	X
ma-136	155	120	(	(	PUNCT
ma-136	155	121	f	f	X
ma-136	155	122	)	)	PUNCT
ma-136	155	123	=	=	SYM
ma-136	156	1	σm,[p	σm,[p	NOUN
ma-136	156	2	,	,	PUNCT
ma-136	156	3	q	q	X
ma-136	156	4	]	]	X
ma-136	156	5	(	(	PUNCT
ma-136	156	6	f	f	X
ma-136	156	7	)	)	PUNCT
ma-136	157	1	=	=	NOUN
ma-136	157	2	∞	∞	NOUN
ma-136	157	3	and	and	CCONJ
ma-136	157	4	σ[p+1,q	σ[p+1,q	NOUN
ma-136	157	5	]	]	PUNCT
ma-136	157	6	(	(	PUNCT
ma-136	157	7	f	f	X
ma-136	157	8	)	)	PUNCT
ma-136	157	9	=	=	SYM
ma-136	158	1	σm,[p+1,q	σm,[p+1,q	X
ma-136	158	2	]	]	PUNCT
ma-136	158	3	(	(	PUNCT
ma-136	158	4	f	f	X
ma-136	158	5	)	)	PUNCT
ma-136	158	6	=	=	PUNCT
ma-136	158	7	µ.	µ.	NOUN
ma-136	158	8	by	by	ADP
ma-136	158	9	theorem	theorem	NOUN
ma-136	158	10	1.1	1.1	NUM
ma-136	158	11	,	,	PUNCT
ma-136	158	12	we	we	PRON
ma-136	158	13	easily	easily	ADV
ma-136	158	14	obtain	obtain	VERB
ma-136	158	15	the	the	DET
ma-136	158	16	following	follow	VERB
ma-136	158	17	corollary	corollary	NOUN
ma-136	158	18	.	.	PUNCT
ma-136	159	1	corollary	corollary	ADJ
ma-136	159	2	1.1	1.1	NUM
ma-136	159	3	(	(	PUNCT
ma-136	159	4	[	[	X
ma-136	159	5	22	22	NUM
ma-136	159	6	]	]	PUNCT
ma-136	159	7	)	)	PUNCT
ma-136	159	8	let	let	VERB
ma-136	159	9	p	p	PRON
ma-136	159	10	≥	≥	PRON
ma-136	159	11	q	q	NOUN
ma-136	159	12	≥	≥	NUM
ma-136	159	13	1	1	NUM
ma-136	159	14	be	be	AUX
ma-136	159	15	integers	integer	NOUN
ma-136	159	16	.	.	PUNCT
ma-136	160	1	let	let	VERB
ma-136	160	2	h	h	PRON
ma-136	160	3	be	be	AUX
ma-136	160	4	a	a	DET
ma-136	160	5	set	set	NOUN
ma-136	160	6	of	of	ADP
ma-136	160	7	complex	complex	ADJ
ma-136	160	8	numbers	number	NOUN
ma-136	160	9	satisfying	satisfy	VERB
ma-136	160	10	densd	densd	PROPN
ma-136	160	11	{	{	PUNCT
ma-136	160	12	|z	|z	PROPN
ma-136	161	1	|	|	ADV
ma-136	161	2	:	:	PUNCT
ma-136	161	3	z	z	PROPN
ma-136	161	4	∈	∈	PROPN
ma-136	161	5	h	h	NOUN
ma-136	162	1	⊆	⊆	NUM
ma-136	162	2	d	d	X
ma-136	162	3	}	}	PUNCT
ma-136	162	4	>	>	X
ma-136	162	5	0	0	NUM
ma-136	162	6	,	,	PUNCT
ma-136	162	7	and	and	CCONJ
ma-136	162	8	let	let	VERB
ma-136	162	9	a0	a0	PROPN
ma-136	162	10	,	,	PUNCT
ma-136	162	11	...	...	PUNCT
ma-136	162	12	,	,	PUNCT
ma-136	162	13	ak−1	ak−1	ADV
ma-136	162	14	be	be	AUX
ma-136	162	15	analytic	analytic	ADJ
ma-136	162	16	functions	function	NOUN
ma-136	162	17	in	in	ADP
ma-136	162	18	the	the	DET
ma-136	162	19	unit	unit	NOUN
ma-136	162	20	disc	disc	VERB
ma-136	162	21	d	d	PROPN
ma-136	162	22	such	such	ADJ
ma-136	162	23	that	that	DET
ma-136	162	24	max	max	PROPN
ma-136	162	25	{	{	PUNCT
ma-136	162	26	σm,[p	σm,[p	PROPN
ma-136	162	27	,	,	PUNCT
ma-136	162	28	q	q	X
ma-136	162	29	]	]	X
ma-136	162	30	(	(	PUNCT
ma-136	162	31	ai	ai	PROPN
ma-136	162	32	)	)	PUNCT
ma-136	162	33	:	:	PUNCT
ma-136	163	1	i	i	NOUN
ma-136	163	2	=	=	NOUN
ma-136	163	3	1	1	NUM
ma-136	163	4	,	,	PUNCT
ma-136	163	5	2	2	NUM
ma-136	163	6	,	,	PUNCT
ma-136	163	7	...	...	PUNCT
ma-136	163	8	,	,	PUNCT
ma-136	163	9	k	k	PROPN
ma-136	163	10	−	−	PROPN
ma-136	163	11	1	1	NUM
ma-136	163	12	}	}	PUNCT
ma-136	163	13	≤	≤	NUM
ma-136	163	14	σm,[p	σm,[p	NOUN
ma-136	163	15	,	,	PUNCT
ma-136	163	16	q	q	X
ma-136	163	17	]	]	X
ma-136	163	18	(	(	PUNCT
ma-136	163	19	a0	a0	PROPN
ma-136	163	20	)	)	PUNCT
ma-136	163	21	=	=	SYM
ma-136	163	22	µ	µ	X
ma-136	163	23	(	(	PUNCT
ma-136	163	24	0	0	NUM
ma-136	163	25	<	<	X
ma-136	163	26	µ	µ	X
ma-136	163	27	<	<	X
ma-136	163	28	+	+	NOUN
ma-136	163	29	∞	∞	NOUN
ma-136	163	30	)	)	PUNCT
ma-136	163	31	and	and	CCONJ
ma-136	163	32	for	for	ADP
ma-136	163	33	some	some	DET
ma-136	163	34	real	real	ADJ
ma-136	163	35	constants	constant	NOUN
ma-136	163	36	α	α	NOUN
ma-136	163	37	,	,	PUNCT
ma-136	163	38	β	β	X
ma-136	163	39	where	where	SCONJ
ma-136	163	40	0	0	NUM
ma-136	163	41	≤	≤	NOUN
ma-136	163	42	β	β	X
ma-136	163	43	<	<	X
ma-136	163	44	α	α	X
ma-136	163	45	,	,	PUNCT
ma-136	163	46	we	we	PRON
ma-136	163	47	have	have	VERB
ma-136	164	1	|a0	|a0	PROPN
ma-136	164	2	(	(	PUNCT
ma-136	164	3	z)|	z)|	PRON
ma-136	164	4	≥	≥	PRON
ma-136	164	5	expp	expp	VERB
ma-136	164	6	{	{	PUNCT
ma-136	164	7	α	α	PROPN
ma-136	164	8	(	(	PUNCT
ma-136	164	9	logq−1	logq−1	X
ma-136	164	10	(	(	PUNCT
ma-136	164	11	1	1	NUM
ma-136	164	12	1−	1−	NUM
ma-136	164	13	|z	|z	NOUN
ma-136	164	14	|	|	ADV
ma-136	164	15	)	)	PUNCT
ma-136	164	16	)	)	PUNCT
ma-136	164	17	µ	µ	X
ma-136	164	18	}	}	PUNCT
ma-136	164	19	and	and	CCONJ
ma-136	164	20	|ai	|ai	NUM
ma-136	164	21	(	(	PUNCT
ma-136	164	22	z)|	z)|	ADP
ma-136	164	23	≤	≤	PROPN
ma-136	164	24	expp	expp	ADJ
ma-136	164	25	{	{	PUNCT
ma-136	164	26	β	β	X
ma-136	164	27	(	(	PUNCT
ma-136	164	28	logq−1	logq−1	X
ma-136	164	29	(	(	PUNCT
ma-136	164	30	1	1	NUM
ma-136	164	31	1−	1−	NUM
ma-136	164	32	|z	|z	NOUN
ma-136	164	33	|	|	ADV
ma-136	164	34	)	)	PUNCT
ma-136	164	35	)	)	PUNCT
ma-136	164	36	µ	µ	X
ma-136	164	37	}	}	PUNCT
ma-136	164	38	,	,	PUNCT
ma-136	164	39	i	i	PRON
ma-136	164	40	=	=	NOUN
ma-136	164	41	1	1	NUM
ma-136	164	42	,	,	PUNCT
ma-136	164	43	...	...	PUNCT
ma-136	164	44	,	,	PUNCT
ma-136	164	45	k	k	PROPN
ma-136	165	1	−	−	PROPN
ma-136	165	2	1	1	NUM
ma-136	165	3	as	as	ADP
ma-136	165	4	|z	|z	PROPN
ma-136	165	5	|	|	PROPN
ma-136	165	6	→	→	SYM
ma-136	165	7	1−	1−	NUM
ma-136	165	8	for	for	ADP
ma-136	165	9	z	z	PROPN
ma-136	165	10	∈	∈	PROPN
ma-136	165	11	h.	h.	NOUN
ma-136	165	12	then	then	ADV
ma-136	165	13	every	every	DET
ma-136	165	14	solution	solution	NOUN
ma-136	165	15	f	f	PROPN
ma-136	165	16	6≡	6≡	NUM
ma-136	165	17	0	0	NUM
ma-136	165	18	of	of	ADP
ma-136	165	19	equation	equation	NOUN
ma-136	165	20	(	(	PUNCT
ma-136	165	21	1.1	1.1	NUM
ma-136	165	22	)	)	PUNCT
ma-136	165	23	satisfies	satisfy	VERB
ma-136	165	24	σ[p	σ[p	NOUN
ma-136	165	25	,	,	PUNCT
ma-136	165	26	q	q	X
ma-136	165	27	]	]	X
ma-136	165	28	(	(	PUNCT
ma-136	165	29	f	f	X
ma-136	165	30	)	)	PUNCT
ma-136	165	31	=	=	SYM
ma-136	166	1	σm,[p	σm,[p	NOUN
ma-136	166	2	,	,	PUNCT
ma-136	166	3	q	q	X
ma-136	166	4	]	]	X
ma-136	166	5	(	(	PUNCT
ma-136	166	6	f	f	X
ma-136	166	7	)	)	PUNCT
ma-136	167	1	=	=	NOUN
ma-136	167	2	∞	∞	NOUN
ma-136	167	3	and	and	CCONJ
ma-136	167	4	σ[p+1,q	σ[p+1,q	NOUN
ma-136	167	5	]	]	PUNCT
ma-136	167	6	(	(	PUNCT
ma-136	167	7	f	f	X
ma-136	167	8	)	)	PUNCT
ma-136	167	9	=	=	SYM
ma-136	168	1	σm,[p+1,q	σm,[p+1,q	X
ma-136	168	2	]	]	PUNCT
ma-136	168	3	(	(	PUNCT
ma-136	168	4	f	f	X
ma-136	168	5	)	)	PUNCT
ma-136	168	6	=	=	SYM
ma-136	168	7	µ.	µ.	NOUN
ma-136	168	8	theorem	theorem	VERB
ma-136	168	9	1.2	1.2	NUM
ma-136	168	10	let	let	VERB
ma-136	168	11	p	p	PRON
ma-136	168	12	≥	≥	PRON
ma-136	168	13	q	q	NOUN
ma-136	168	14	≥	≥	NUM
ma-136	168	15	1	1	NUM
ma-136	168	16	be	be	AUX
ma-136	168	17	integers	integer	NOUN
ma-136	168	18	.	.	PUNCT
ma-136	169	1	let	let	VERB
ma-136	169	2	h	h	PRON
ma-136	169	3	be	be	AUX
ma-136	169	4	a	a	DET
ma-136	169	5	set	set	NOUN
ma-136	169	6	of	of	ADP
ma-136	169	7	complex	complex	ADJ
ma-136	169	8	numbers	number	NOUN
ma-136	169	9	satisfying	satisfy	VERB
ma-136	169	10	densd	densd	PROPN
ma-136	169	11	{	{	PUNCT
ma-136	169	12	|z	|z	PROPN
ma-136	170	1	|	|	ADV
ma-136	170	2	:	:	PUNCT
ma-136	170	3	z	z	PROPN
ma-136	170	4	∈	∈	PROPN
ma-136	170	5	h	h	NOUN
ma-136	171	1	⊆	⊆	NUM
ma-136	171	2	d	d	X
ma-136	171	3	}	}	PUNCT
ma-136	171	4	>	>	X
ma-136	171	5	0	0	NUM
ma-136	171	6	,	,	PUNCT
ma-136	171	7	and	and	CCONJ
ma-136	171	8	let	let	VERB
ma-136	171	9	a0	a0	PROPN
ma-136	171	10	,	,	PUNCT
ma-136	171	11	...	...	PUNCT
ma-136	171	12	,	,	PUNCT
ma-136	171	13	ak−1	ak−1	ADV
ma-136	171	14	be	be	AUX
ma-136	171	15	analytic	analytic	ADJ
ma-136	171	16	functions	function	NOUN
ma-136	171	17	in	in	ADP
ma-136	171	18	the	the	DET
ma-136	171	19	unit	unit	NOUN
ma-136	171	20	disc	disc	VERB
ma-136	171	21	d	d	PROPN
ma-136	171	22	such	such	ADJ
ma-136	171	23	that	that	DET
ma-136	171	24	max	max	PROPN
ma-136	171	25	{	{	PUNCT
ma-136	171	26	σm,[p	σm,[p	PROPN
ma-136	171	27	,	,	PUNCT
ma-136	171	28	q	q	X
ma-136	171	29	]	]	X
ma-136	171	30	(	(	PUNCT
ma-136	171	31	ai	ai	PROPN
ma-136	171	32	)	)	PUNCT
ma-136	171	33	:	:	PUNCT
ma-136	172	1	i	i	NOUN
ma-136	172	2	=	=	NOUN
ma-136	172	3	1	1	NUM
ma-136	172	4	,	,	PUNCT
ma-136	172	5	2	2	NUM
ma-136	172	6	,	,	PUNCT
ma-136	172	7	...	...	PUNCT
ma-136	172	8	,	,	PUNCT
ma-136	172	9	k	k	PROPN
ma-136	172	10	−	−	PROPN
ma-136	172	11	1	1	NUM
ma-136	172	12	}	}	PUNCT
ma-136	172	13	≤	≤	NUM
ma-136	172	14	σm,[p	σm,[p	NOUN
ma-136	172	15	,	,	PUNCT
ma-136	172	16	q	q	X
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ma-136	172	18	(	(	PUNCT
ma-136	172	19	a0	a0	PROPN
ma-136	172	20	)	)	PUNCT
ma-136	172	21	=	=	SYM
ma-136	172	22	µ	µ	X
ma-136	172	23	(	(	PUNCT
ma-136	172	24	0	0	NUM
ma-136	172	25	<	<	X
ma-136	172	26	µ	µ	X
ma-136	172	27	<	<	X
ma-136	172	28	+	+	NOUN
ma-136	172	29	∞	∞	NUM
ma-136	172	30	)	)	PUNCT
ma-136	172	31	and	and	CCONJ
ma-136	172	32	lim	lim	PROPN
ma-136	172	33	sup	sup	PROPN
ma-136	172	34	|z	|z	PROPN
ma-136	172	35	|→1−,z∈h	|→1−,z∈h	PROPN
ma-136	172	36	logp	logp	NOUN
ma-136	172	37	|ai	|ai	NUM
ma-136	172	38	(	(	PUNCT
ma-136	172	39	z)|	z)|	X
ma-136	172	40	(	(	PUNCT
ma-136	172	41	logq−1	logq−1	X
ma-136	172	42	(	(	PUNCT
ma-136	172	43	1	1	NUM
ma-136	172	44	1−|z	1−|z	NUM
ma-136	172	45	|	|	NOUN
ma-136	172	46	)	)	PUNCT
ma-136	172	47	)	)	PUNCT
ma-136	172	48	µ	µ	X
ma-136	172	49	<	<	X
ma-136	172	50	lim	lim	PROPN
ma-136	172	51	inf	inf	PROPN
ma-136	172	52	|z	|z	PROPN
ma-136	172	53	|→1−,z∈h	|→1−,z∈h	PROPN
ma-136	172	54	logp	logp	NOUN
ma-136	172	55	|a0	|a0	PROPN
ma-136	172	56	(	(	PUNCT
ma-136	172	57	z)|	z)|	X
ma-136	172	58	(	(	PUNCT
ma-136	172	59	logq−1	logq−1	X
ma-136	172	60	(	(	PUNCT
ma-136	172	61	1	1	NUM
ma-136	172	62	1−|z	1−|z	NUM
ma-136	172	63	|	|	NOUN
ma-136	172	64	)	)	PUNCT
ma-136	172	65	)	)	PUNCT
ma-136	172	66	µ	µ	X
ma-136	172	67	(	(	PUNCT
ma-136	172	68	i	i	NOUN
ma-136	172	69	=	=	NOUN
ma-136	172	70	1	1	NUM
ma-136	172	71	,	,	PUNCT
ma-136	172	72	...	...	PUNCT
ma-136	172	73	,	,	PUNCT
ma-136	172	74	k	k	PROPN
ma-136	173	1	−	−	PROPN
ma-136	173	2	1	1	NUM
ma-136	173	3	)	)	PUNCT
ma-136	173	4	(	(	PUNCT
ma-136	173	5	1.5	1.5	NUM
ma-136	173	6	)	)	PUNCT
ma-136	173	7	https://doi.org/10.28924/ada/ma.3.10	https://doi.org/10.28924/ada/ma.3.10	ADV
ma-136	173	8	eur	eur	PROPN
ma-136	173	9	.	.	PUNCT
ma-136	174	1	j.	j.	PROPN
ma-136	174	2	math	math	PROPN
ma-136	174	3	.	.	PUNCT
ma-136	175	1	anal	anal	PROPN
ma-136	175	2	.	.	PUNCT
ma-136	176	1	10.28924	10.28924	NUM
ma-136	176	2	/	/	SYM
ma-136	176	3	ada	ada	NOUN
ma-136	176	4	/	/	NOUN
ma-136	176	5	ma.3.10	ma.3.10	ADJ
ma-136	176	6	7	7	NUM
ma-136	176	7	as	as	ADP
ma-136	176	8	|z	|z	PROPN
ma-136	176	9	|	|	PROPN
ma-136	176	10	→	→	SYM
ma-136	176	11	1−	1−	NUM
ma-136	176	12	for	for	ADP
ma-136	176	13	z	z	PROPN
ma-136	176	14	∈	∈	PROPN
ma-136	176	15	h.then	h.then	ADP
ma-136	176	16	every	every	DET
ma-136	176	17	solution	solution	NOUN
ma-136	176	18	f	f	PROPN
ma-136	176	19	6≡	6≡	NUM
ma-136	176	20	0	0	NUM
ma-136	176	21	of	of	ADP
ma-136	176	22	equation	equation	NOUN
ma-136	176	23	(	(	PUNCT
ma-136	176	24	1.1	1.1	NUM
ma-136	176	25	)	)	PUNCT
ma-136	176	26	satisfies	satisfy	VERB
ma-136	176	27	σ[p	σ[p	NOUN
ma-136	176	28	,	,	PUNCT
ma-136	176	29	q	q	X
ma-136	176	30	]	]	X
ma-136	176	31	(	(	PUNCT
ma-136	176	32	f	f	X
ma-136	176	33	)	)	PUNCT
ma-136	176	34	=	=	SYM
ma-136	177	1	σm,[p	σm,[p	NOUN
ma-136	177	2	,	,	PUNCT
ma-136	177	3	q	q	X
ma-136	177	4	]	]	X
ma-136	177	5	(	(	PUNCT
ma-136	177	6	f	f	X
ma-136	177	7	)	)	PUNCT
ma-136	178	1	=	=	NOUN
ma-136	178	2	∞	∞	NOUN
ma-136	178	3	and	and	CCONJ
ma-136	178	4	σ[p+1,q	σ[p+1,q	NOUN
ma-136	178	5	]	]	PUNCT
ma-136	178	6	(	(	PUNCT
ma-136	178	7	f	f	X
ma-136	178	8	)	)	PUNCT
ma-136	178	9	=	=	SYM
ma-136	179	1	σm,[p+1,q	σm,[p+1,q	X
ma-136	179	2	]	]	PUNCT
ma-136	179	3	(	(	PUNCT
ma-136	179	4	f	f	X
ma-136	179	5	)	)	PUNCT
ma-136	179	6	=	=	SYM
ma-136	179	7	µ.	µ.	NOUN
ma-136	179	8	theorem	theorem	VERB
ma-136	179	9	1.3	1.3	NUM
ma-136	179	10	let	let	VERB
ma-136	179	11	p	p	PRON
ma-136	179	12	≥	≥	PRON
ma-136	179	13	q	q	NOUN
ma-136	179	14	≥	≥	NUM
ma-136	179	15	1	1	NUM
ma-136	179	16	be	be	AUX
ma-136	179	17	integers	integer	NOUN
ma-136	179	18	.	.	PUNCT
ma-136	180	1	let	let	VERB
ma-136	180	2	h	h	PRON
ma-136	180	3	be	be	AUX
ma-136	180	4	a	a	DET
ma-136	180	5	set	set	NOUN
ma-136	180	6	of	of	ADP
ma-136	180	7	complex	complex	ADJ
ma-136	180	8	numbers	number	NOUN
ma-136	180	9	satisfying	satisfy	VERB
ma-136	180	10	densd	densd	PROPN
ma-136	180	11	{	{	PUNCT
ma-136	180	12	|z	|z	PROPN
ma-136	181	1	|	|	ADV
ma-136	181	2	:	:	PUNCT
ma-136	181	3	z	z	PROPN
ma-136	181	4	∈	∈	PROPN
ma-136	181	5	h	h	NOUN
ma-136	182	1	⊆	⊆	NUM
ma-136	182	2	d	d	X
ma-136	182	3	}	}	PUNCT
ma-136	182	4	>	>	X
ma-136	182	5	0	0	NUM
ma-136	182	6	,	,	PUNCT
ma-136	182	7	and	and	CCONJ
ma-136	182	8	let	let	VERB
ma-136	182	9	a0	a0	PROPN
ma-136	182	10	,	,	PUNCT
ma-136	182	11	...	...	PUNCT
ma-136	182	12	,	,	PUNCT
ma-136	182	13	ak−1	ak−1	ADV
ma-136	182	14	be	be	AUX
ma-136	182	15	analytic	analytic	ADJ
ma-136	182	16	functions	function	NOUN
ma-136	182	17	in	in	ADP
ma-136	182	18	the	the	DET
ma-136	182	19	unit	unit	NOUN
ma-136	182	20	disc	disc	VERB
ma-136	182	21	d	d	PROPN
ma-136	182	22	such	such	ADJ
ma-136	182	23	that	that	DET
ma-136	182	24	max	max	PROPN
ma-136	182	25	{	{	PUNCT
ma-136	182	26	σm,[p	σm,[p	PROPN
ma-136	182	27	,	,	PUNCT
ma-136	182	28	q	q	X
ma-136	182	29	]	]	X
ma-136	182	30	(	(	PUNCT
ma-136	182	31	ai	ai	PROPN
ma-136	182	32	)	)	PUNCT
ma-136	182	33	:	:	PUNCT
ma-136	183	1	i	i	NOUN
ma-136	183	2	=	=	NOUN
ma-136	183	3	1	1	NUM
ma-136	183	4	,	,	PUNCT
ma-136	183	5	2	2	NUM
ma-136	183	6	,	,	PUNCT
ma-136	183	7	...	...	PUNCT
ma-136	183	8	,	,	PUNCT
ma-136	183	9	k	k	PROPN
ma-136	183	10	−	−	PROPN
ma-136	183	11	1	1	NUM
ma-136	183	12	}	}	PUNCT
ma-136	183	13	≤	≤	NUM
ma-136	183	14	σm,[p	σm,[p	NOUN
ma-136	183	15	,	,	PUNCT
ma-136	183	16	q	q	X
ma-136	183	17	]	]	X
ma-136	183	18	(	(	PUNCT
ma-136	183	19	a0	a0	PROPN
ma-136	183	20	)	)	PUNCT
ma-136	183	21	=	=	SYM
ma-136	183	22	µ	µ	X
ma-136	183	23	(	(	PUNCT
ma-136	183	24	0	0	NUM
ma-136	183	25	<	<	X
ma-136	183	26	µ	µ	X
ma-136	183	27	<	<	X
ma-136	183	28	+	+	NOUN
ma-136	183	29	∞	∞	NOUN
ma-136	183	30	)	)	PUNCT
ma-136	183	31	and	and	CCONJ
ma-136	183	32	for	for	ADP
ma-136	183	33	a	a	DET
ma-136	183	34	constant	constant	ADJ
ma-136	183	35	α	α	PRON
ma-136	183	36	≥	≥	NOUN
ma-136	183	37	0	0	NUM
ma-136	183	38	,	,	PUNCT
ma-136	183	39	if	if	SCONJ
ma-136	183	40	p	p	PROPN
ma-136	183	41	≥	≥	PUNCT
ma-136	183	42	q	q	X
ma-136	183	43	≥	≥	NUM
ma-136	183	44	2	2	NUM
ma-136	183	45	we	we	PRON
ma-136	183	46	have	have	VERB
ma-136	183	47	lim	lim	PROPN
ma-136	183	48	inf	inf	PROPN
ma-136	183	49	|z	|z	PROPN
ma-136	183	50	|→1−,z∈h	|→1−,z∈h	PROPN
ma-136	183	51	logp−1	logp−1	PROPN
ma-136	183	52	t	t	PROPN
ma-136	183	53	(	(	PUNCT
ma-136	183	54	r	r	PROPN
ma-136	183	55	,	,	PUNCT
ma-136	183	56	a0	a0	NOUN
ma-136	183	57	)	)	PUNCT
ma-136	183	58	(	(	PUNCT
ma-136	183	59	logq−1	logq−1	X
ma-136	183	60	(	(	PUNCT
ma-136	183	61	1	1	NUM
ma-136	183	62	1−|z	1−|z	NUM
ma-136	183	63	|	|	NOUN
ma-136	183	64	)	)	PUNCT
ma-136	183	65	)	)	PUNCT
ma-136	183	66	µ	µ	X
ma-136	183	67	>	>	X
ma-136	183	68	α	α	PROPN
ma-136	183	69	(	(	PUNCT
ma-136	183	70	1.6	1.6	NUM
ma-136	183	71	)	)	PUNCT
ma-136	183	72	and	and	CCONJ
ma-136	183	73	t	t	PROPN
ma-136	183	74	(	(	PUNCT
ma-136	183	75	r	r	NOUN
ma-136	183	76	,	,	PUNCT
ma-136	183	77	ai	ai	NOUN
ma-136	183	78	)	)	PUNCT
ma-136	183	79	≤	≤	NOUN
ma-136	183	80	expp−1	expp−1	PROPN
ma-136	183	81	{	{	PUNCT
ma-136	183	82	α	α	PROPN
ma-136	183	83	(	(	PUNCT
ma-136	183	84	logq−1	logq−1	X
ma-136	183	85	(	(	PUNCT
ma-136	183	86	1	1	NUM
ma-136	183	87	1−|z	1−|z	NUM
ma-136	183	88	|	|	NOUN
ma-136	183	89	)	)	PUNCT
ma-136	183	90	)	)	PUNCT
ma-136	183	91	µ	µ	X
ma-136	183	92	}	}	PUNCT
ma-136	183	93	,	,	PUNCT
ma-136	183	94	(	(	PUNCT
ma-136	183	95	i	i	NOUN
ma-136	183	96	=	=	NOUN
ma-136	183	97	1	1	NUM
ma-136	183	98	,	,	PUNCT
ma-136	183	99	...	...	PUNCT
ma-136	183	100	,	,	PUNCT
ma-136	183	101	k	k	PROPN
ma-136	184	1	−	−	PROPN
ma-136	184	2	1	1	NUM
ma-136	184	3	)	)	PUNCT
ma-136	184	4	(	(	PUNCT
ma-136	184	5	1.7	1.7	NUM
ma-136	184	6	)	)	PUNCT
ma-136	184	7	as	as	ADP
ma-136	184	8	|z	|z	PROPN
ma-136	184	9	|	|	ADV
ma-136	184	10	=	=	SYM
ma-136	184	11	r	r	NOUN
ma-136	184	12	→	→	SYM
ma-136	184	13	1−	1−	NUM
ma-136	184	14	for	for	ADP
ma-136	184	15	z	z	PROPN
ma-136	184	16	∈	∈	PROPN
ma-136	184	17	h	h	NOUN
ma-136	184	18	,	,	PUNCT
ma-136	184	19	then	then	ADV
ma-136	184	20	every	every	DET
ma-136	184	21	solution	solution	NOUN
ma-136	184	22	f	f	PROPN
ma-136	184	23	6≡	6≡	NUM
ma-136	184	24	0	0	NUM
ma-136	184	25	of	of	ADP
ma-136	184	26	equation	equation	NOUN
ma-136	184	27	(	(	PUNCT
ma-136	184	28	1.1	1.1	NUM
ma-136	184	29	)	)	PUNCT
ma-136	184	30	satisfies	satisfy	VERB
ma-136	184	31	σ[p	σ[p	NOUN
ma-136	184	32	,	,	PUNCT
ma-136	184	33	q	q	X
ma-136	184	34	]	]	X
ma-136	184	35	(	(	PUNCT
ma-136	184	36	f	f	X
ma-136	184	37	)	)	PUNCT
ma-136	184	38	=	=	SYM
ma-136	185	1	σm,[p	σm,[p	NOUN
ma-136	185	2	,	,	PUNCT
ma-136	185	3	q	q	X
ma-136	185	4	]	]	X
ma-136	185	5	(	(	PUNCT
ma-136	185	6	f	f	X
ma-136	185	7	)	)	PUNCT
ma-136	186	1	=	=	NOUN
ma-136	186	2	∞	∞	NOUN
ma-136	186	3	and	and	CCONJ
ma-136	186	4	σ[p+1,q	σ[p+1,q	NOUN
ma-136	186	5	]	]	PUNCT
ma-136	186	6	(	(	PUNCT
ma-136	186	7	f	f	X
ma-136	186	8	)	)	PUNCT
ma-136	186	9	=	=	SYM
ma-136	187	1	σm,[p+1,q	σm,[p+1,q	X
ma-136	187	2	]	]	PUNCT
ma-136	187	3	(	(	PUNCT
ma-136	187	4	f	f	X
ma-136	187	5	)	)	PUNCT
ma-136	187	6	=	=	PUNCT
ma-136	188	1	µ.	µ.	NOUN
ma-136	188	2	if	if	SCONJ
ma-136	188	3	p	p	NOUN
ma-136	188	4	=	=	X
ma-136	188	5	q	q	NOUN
ma-136	188	6	=	=	NOUN
ma-136	188	7	1	1	NUM
ma-136	188	8	,	,	PUNCT
ma-136	188	9	we	we	PRON
ma-136	188	10	have	have	VERB
ma-136	188	11	lim	lim	PROPN
ma-136	188	12	inf	inf	PROPN
ma-136	188	13	|z	|z	PROPN
ma-136	188	14	|→1−,z∈h	|→1−,z∈h	PROPN
ma-136	188	15	t	t	PROPN
ma-136	188	16	(	(	PUNCT
ma-136	188	17	r	r	PROPN
ma-136	188	18	,	,	PUNCT
ma-136	188	19	a0	a0	NOUN
ma-136	188	20	)	)	PUNCT
ma-136	188	21	(	(	PUNCT
ma-136	188	22	1	1	NUM
ma-136	188	23	1−|z	1−|z	NUM
ma-136	188	24	|	|	NOUN
ma-136	188	25	)	)	PUNCT
ma-136	188	26	µ	µ	X
ma-136	188	27	>	>	X
ma-136	189	1	(	(	PUNCT
ma-136	189	2	k	k	PROPN
ma-136	189	3	−	−	PROPN
ma-136	189	4	1)α	1)α	NUM
ma-136	189	5	(	(	PUNCT
ma-136	189	6	1.8	1.8	NUM
ma-136	189	7	)	)	PUNCT
ma-136	189	8	and	and	CCONJ
ma-136	189	9	t	t	PROPN
ma-136	189	10	(	(	PUNCT
ma-136	189	11	r	r	NOUN
ma-136	189	12	,	,	PUNCT
ma-136	189	13	ai	ai	NOUN
ma-136	189	14	)	)	PUNCT
ma-136	189	15	≤	≤	NOUN
ma-136	189	16	α	α	PROPN
ma-136	189	17	(	(	PUNCT
ma-136	189	18	1	1	NUM
ma-136	189	19	1−|z	1−|z	NUM
ma-136	189	20	|	|	ADJ
ma-136	189	21	)	)	PUNCT
ma-136	189	22	µ	µ	NOUN
ma-136	189	23	,	,	PUNCT
ma-136	189	24	(	(	PUNCT
ma-136	189	25	i	i	NOUN
ma-136	189	26	=	=	NOUN
ma-136	189	27	1	1	NUM
ma-136	189	28	,	,	PUNCT
ma-136	189	29	...	...	PUNCT
ma-136	189	30	,	,	PUNCT
ma-136	189	31	k	k	PROPN
ma-136	190	1	−	−	PROPN
ma-136	190	2	1	1	NUM
ma-136	190	3	)	)	PUNCT
ma-136	190	4	(	(	PUNCT
ma-136	190	5	1.9	1.9	NUM
ma-136	190	6	)	)	PUNCT
ma-136	190	7	as	as	ADP
ma-136	190	8	|z	|z	PROPN
ma-136	190	9	|	|	ADV
ma-136	190	10	=	=	SYM
ma-136	190	11	r	r	NOUN
ma-136	190	12	→	→	SYM
ma-136	190	13	1−	1−	NUM
ma-136	190	14	for	for	ADP
ma-136	190	15	z	z	PROPN
ma-136	190	16	∈	∈	PROPN
ma-136	190	17	h	h	NOUN
ma-136	190	18	,	,	PUNCT
ma-136	190	19	then	then	ADV
ma-136	190	20	every	every	DET
ma-136	190	21	nontrivial	nontrivial	ADJ
ma-136	190	22	solution	solution	NOUN
ma-136	190	23	f	f	PROPN
ma-136	190	24	of	of	ADP
ma-136	190	25	equation	equation	NOUN
ma-136	190	26	(	(	PUNCT
ma-136	190	27	1.1	1.1	NUM
ma-136	190	28	)	)	PUNCT
ma-136	190	29	satisfies	satisfie	NOUN
ma-136	190	30	σ(f	σ(f	ADV
ma-136	190	31	)	)	PUNCT
ma-136	190	32	=	=	SYM
ma-136	190	33	σm(f	σm(f	NOUN
ma-136	190	34	)	)	PUNCT
ma-136	191	1	=	=	SYM
ma-136	191	2	∞	∞	PROPN
ma-136	191	3	and	and	CCONJ
ma-136	191	4	σ2	σ2	PROPN
ma-136	191	5	(	(	PUNCT
ma-136	191	6	f	f	PROPN
ma-136	191	7	)	)	PUNCT
ma-136	192	1	=	=	SYM
ma-136	192	2	σm,2	σm,2	PROPN
ma-136	192	3	(	(	PUNCT
ma-136	192	4	f	f	X
ma-136	192	5	)	)	PUNCT
ma-136	192	6	=	=	PUNCT
ma-136	192	7	µ.	µ.	NOUN
ma-136	192	8	by	by	ADP
ma-136	192	9	theorem	theorem	NOUN
ma-136	192	10	1.3	1.3	NUM
ma-136	192	11	,	,	PUNCT
ma-136	192	12	we	we	PRON
ma-136	192	13	easily	easily	ADV
ma-136	192	14	obtain	obtain	VERB
ma-136	192	15	the	the	DET
ma-136	192	16	following	follow	VERB
ma-136	192	17	corollary	corollary	NOUN
ma-136	192	18	.	.	PUNCT
ma-136	193	1	corollary	corollary	ADJ
ma-136	193	2	1.2	1.2	NUM
ma-136	193	3	(	(	PUNCT
ma-136	193	4	[	[	X
ma-136	193	5	22	22	NUM
ma-136	193	6	]	]	PUNCT
ma-136	193	7	)	)	PUNCT
ma-136	193	8	let	let	VERB
ma-136	193	9	p	p	PRON
ma-136	193	10	≥	≥	PRON
ma-136	193	11	q	q	NOUN
ma-136	193	12	≥	≥	NUM
ma-136	193	13	1	1	NUM
ma-136	193	14	be	be	AUX
ma-136	193	15	integers	integer	NOUN
ma-136	193	16	.	.	PUNCT
ma-136	194	1	let	let	VERB
ma-136	194	2	h	h	PRON
ma-136	194	3	be	be	AUX
ma-136	194	4	a	a	DET
ma-136	194	5	set	set	NOUN
ma-136	194	6	of	of	ADP
ma-136	194	7	complex	complex	ADJ
ma-136	194	8	numbers	number	NOUN
ma-136	194	9	satisfying	satisfy	VERB
ma-136	194	10	densd	densd	PROPN
ma-136	194	11	{	{	PUNCT
ma-136	194	12	|z	|z	PROPN
ma-136	195	1	|	|	ADV
ma-136	195	2	:	:	PUNCT
ma-136	195	3	z	z	PROPN
ma-136	195	4	∈	∈	PROPN
ma-136	195	5	h	h	NOUN
ma-136	196	1	⊆	⊆	NUM
ma-136	196	2	d	d	X
ma-136	196	3	}	}	PUNCT
ma-136	196	4	>	>	X
ma-136	196	5	0	0	NUM
ma-136	196	6	,	,	PUNCT
ma-136	196	7	and	and	CCONJ
ma-136	196	8	let	let	VERB
ma-136	196	9	a0	a0	PROPN
ma-136	196	10	,	,	PUNCT
ma-136	196	11	...	...	PUNCT
ma-136	196	12	,	,	PUNCT
ma-136	196	13	ak−1	ak−1	ADV
ma-136	196	14	be	be	AUX
ma-136	196	15	analytic	analytic	ADJ
ma-136	196	16	functions	function	NOUN
ma-136	196	17	in	in	ADP
ma-136	196	18	the	the	DET
ma-136	196	19	unit	unit	NOUN
ma-136	196	20	disc	disc	VERB
ma-136	196	21	d	d	PROPN
ma-136	196	22	such	such	ADJ
ma-136	196	23	that	that	DET
ma-136	196	24	max	max	PROPN
ma-136	196	25	{	{	PUNCT
ma-136	196	26	σm,[p	σm,[p	PROPN
ma-136	196	27	,	,	PUNCT
ma-136	196	28	q	q	X
ma-136	196	29	]	]	X
ma-136	196	30	(	(	PUNCT
ma-136	196	31	ai	ai	PROPN
ma-136	196	32	)	)	PUNCT
ma-136	196	33	:	:	PUNCT
ma-136	197	1	i	i	NOUN
ma-136	197	2	=	=	NOUN
ma-136	197	3	1	1	NUM
ma-136	197	4	,	,	PUNCT
ma-136	197	5	2	2	NUM
ma-136	197	6	,	,	PUNCT
ma-136	197	7	...	...	PUNCT
ma-136	197	8	,	,	PUNCT
ma-136	197	9	k	k	PROPN
ma-136	197	10	−	−	PROPN
ma-136	197	11	1	1	NUM
ma-136	197	12	}	}	PUNCT
ma-136	197	13	≤	≤	NUM
ma-136	197	14	σm,[p	σm,[p	NOUN
ma-136	197	15	,	,	PUNCT
ma-136	197	16	q	q	X
ma-136	197	17	]	]	X
ma-136	197	18	(	(	PUNCT
ma-136	197	19	a0	a0	PROPN
ma-136	197	20	)	)	PUNCT
ma-136	197	21	=	=	SYM
ma-136	197	22	µ	µ	X
ma-136	197	23	(	(	PUNCT
ma-136	197	24	0	0	NUM
ma-136	197	25	<	<	X
ma-136	197	26	µ	µ	X
ma-136	197	27	<	<	X
ma-136	197	28	+	+	NOUN
ma-136	197	29	∞	∞	NOUN
ma-136	197	30	)	)	PUNCT
ma-136	197	31	and	and	CCONJ
ma-136	197	32	for	for	ADP
ma-136	197	33	some	some	DET
ma-136	197	34	real	real	ADJ
ma-136	197	35	constants	constant	NOUN
ma-136	197	36	α	α	NOUN
ma-136	197	37	,	,	PUNCT
ma-136	197	38	β	β	NOUN
ma-136	197	39	,	,	PUNCT
ma-136	197	40	where	where	SCONJ
ma-136	197	41	0	0	NUM
ma-136	197	42	≤	≤	NOUN
ma-136	197	43	β	β	X
ma-136	197	44	<	<	X
ma-136	197	45	α	α	X
ma-136	197	46	,	,	PUNCT
ma-136	197	47	we	we	PRON
ma-136	197	48	have	have	VERB
ma-136	197	49	t	t	NOUN
ma-136	197	50	(	(	PUNCT
ma-136	197	51	r	r	NOUN
ma-136	197	52	,	,	PUNCT
ma-136	197	53	a0	a0	PROPN
ma-136	197	54	)	)	PUNCT
ma-136	197	55	≥	≥	NOUN
ma-136	198	1	expp−1	expp−1	NOUN
ma-136	198	2	{	{	PUNCT
ma-136	198	3	α	α	PROPN
ma-136	198	4	(	(	PUNCT
ma-136	198	5	logq−1	logq−1	X
ma-136	198	6	(	(	PUNCT
ma-136	198	7	1	1	NUM
ma-136	198	8	1−	1−	NUM
ma-136	198	9	|z	|z	NOUN
ma-136	198	10	|	|	ADV
ma-136	198	11	)	)	PUNCT
ma-136	198	12	)	)	PUNCT
ma-136	198	13	µ	µ	X
ma-136	198	14	}	}	PUNCT
ma-136	198	15	and	and	CCONJ
ma-136	198	16	t	t	PROPN
ma-136	198	17	(	(	PUNCT
ma-136	198	18	r	r	NOUN
ma-136	198	19	,	,	PUNCT
ma-136	198	20	ai	ai	NOUN
ma-136	198	21	)	)	PUNCT
ma-136	198	22	≤	≤	NOUN
ma-136	198	23	expp−1	expp−1	PROPN
ma-136	198	24	{	{	PUNCT
ma-136	198	25	β	β	X
ma-136	198	26	(	(	PUNCT
ma-136	198	27	logq−1	logq−1	X
ma-136	198	28	(	(	PUNCT
ma-136	198	29	1	1	NUM
ma-136	198	30	1−|z	1−|z	NUM
ma-136	198	31	|	|	NOUN
ma-136	198	32	)	)	PUNCT
ma-136	198	33	)	)	PUNCT
ma-136	198	34	µ	µ	X
ma-136	198	35	}	}	PUNCT
ma-136	198	36	(	(	PUNCT
ma-136	198	37	i	i	NOUN
ma-136	198	38	=	=	NOUN
ma-136	198	39	1	1	NUM
ma-136	198	40	,	,	PUNCT
ma-136	198	41	...	...	PUNCT
ma-136	198	42	,	,	PUNCT
ma-136	198	43	k	k	PROPN
ma-136	199	1	−	−	PROPN
ma-136	199	2	1	1	NUM
ma-136	199	3	)	)	PUNCT
ma-136	199	4	as	as	ADP
ma-136	199	5	|z	|z	PROPN
ma-136	199	6	|	|	ADV
ma-136	199	7	=	=	SYM
ma-136	199	8	r	r	NOUN
ma-136	199	9	→	→	SYM
ma-136	199	10	1−	1−	NUM
ma-136	199	11	for	for	ADP
ma-136	199	12	z	z	PROPN
ma-136	199	13	∈	∈	PROPN
ma-136	199	14	h.	h.	NOUN
ma-136	199	15	then	then	ADV
ma-136	199	16	the	the	DET
ma-136	199	17	following	follow	VERB
ma-136	199	18	statements	statement	NOUN
ma-136	199	19	hold	hold	VERB
ma-136	199	20	:	:	PUNCT
ma-136	199	21	https://doi.org/10.28924/ada/ma.3.10	https://doi.org/10.28924/ada/ma.3.10	ADJ
ma-136	199	22	eur	eur	PROPN
ma-136	199	23	.	.	PUNCT
ma-136	200	1	j.	j.	PROPN
ma-136	200	2	math	math	PROPN
ma-136	200	3	.	.	PUNCT
ma-136	201	1	anal	anal	PROPN
ma-136	201	2	.	.	PUNCT
ma-136	202	1	10.28924	10.28924	NUM
ma-136	202	2	/	/	SYM
ma-136	202	3	ada	ada	NOUN
ma-136	202	4	/	/	SYM
ma-136	202	5	ma.3.10	ma.3.10	ADJ
ma-136	202	6	8	8	NUM
ma-136	202	7	(	(	PUNCT
ma-136	202	8	i	i	NOUN
ma-136	202	9	)	)	PUNCT
ma-136	202	10	if	if	SCONJ
ma-136	202	11	p	p	NOUN
ma-136	202	12	=	=	X
ma-136	202	13	q	q	NOUN
ma-136	202	14	=	=	SYM
ma-136	202	15	1	1	NUM
ma-136	202	16	and	and	CCONJ
ma-136	202	17	0	0	NUM
ma-136	202	18	≤	≤	NOUN
ma-136	202	19	(	(	PUNCT
ma-136	202	20	k	k	NOUN
ma-136	202	21	−	−	PROPN
ma-136	202	22	1)β	1)β	ADP
ma-136	202	23	<	<	X
ma-136	202	24	α	α	NOUN
ma-136	202	25	,	,	PUNCT
ma-136	202	26	then	then	ADV
ma-136	202	27	every	every	DET
ma-136	202	28	nontrivial	nontrivial	ADJ
ma-136	202	29	solution	solution	NOUN
ma-136	202	30	f	f	PROPN
ma-136	202	31	of	of	ADP
ma-136	202	32	equation	equation	NOUN
ma-136	202	33	(	(	PUNCT
ma-136	202	34	1.1	1.1	NUM
ma-136	202	35	)	)	PUNCT
ma-136	202	36	satisfies	satisfie	NOUN
ma-136	202	37	σ(f	σ(f	ADV
ma-136	202	38	)	)	PUNCT
ma-136	203	1	=	=	SYM
ma-136	203	2	σm(f	σm(f	NOUN
ma-136	203	3	)	)	PUNCT
ma-136	204	1	=	=	SYM
ma-136	204	2	∞	∞	PROPN
ma-136	204	3	and	and	CCONJ
ma-136	204	4	σ2	σ2	PROPN
ma-136	204	5	(	(	PUNCT
ma-136	204	6	f	f	PROPN
ma-136	204	7	)	)	PUNCT
ma-136	205	1	=	=	SYM
ma-136	205	2	σm,2	σm,2	PROPN
ma-136	205	3	(	(	PUNCT
ma-136	205	4	f	f	X
ma-136	205	5	)	)	PUNCT
ma-136	205	6	=	=	SYM
ma-136	205	7	µ.	µ.	NOUN
ma-136	205	8	(	(	PUNCT
ma-136	205	9	ii	ii	NOUN
ma-136	205	10	)	)	PUNCT
ma-136	205	11	if	if	SCONJ
ma-136	205	12	p	p	PROPN
ma-136	205	13	≥	≥	PUNCT
ma-136	205	14	q	q	NOUN
ma-136	205	15	≥	≥	NUM
ma-136	205	16	2	2	NUM
ma-136	205	17	and	and	CCONJ
ma-136	205	18	0	0	NUM
ma-136	205	19	≤	≤	NUM
ma-136	205	20	β	β	X
ma-136	205	21	<	<	X
ma-136	205	22	α	α	X
ma-136	205	23	,	,	PUNCT
ma-136	205	24	then	then	ADV
ma-136	205	25	every	every	DET
ma-136	205	26	nontrivial	nontrivial	ADJ
ma-136	205	27	solution	solution	NOUN
ma-136	205	28	f	f	PROPN
ma-136	205	29	of	of	ADP
ma-136	205	30	equation	equation	NOUN
ma-136	205	31	(	(	PUNCT
ma-136	205	32	1.1	1.1	NUM
ma-136	205	33	)	)	PUNCT
ma-136	205	34	satisfies	satisfy	VERB
ma-136	205	35	σ[p	σ[p	NOUN
ma-136	205	36	,	,	PUNCT
ma-136	205	37	q	q	X
ma-136	205	38	]	]	X
ma-136	205	39	(	(	PUNCT
ma-136	205	40	f	f	X
ma-136	205	41	)	)	PUNCT
ma-136	205	42	=	=	SYM
ma-136	205	43	σm,[p	σm,[p	NOUN
ma-136	205	44	,	,	PUNCT
ma-136	205	45	q	q	X
ma-136	205	46	]	]	X
ma-136	205	47	(	(	PUNCT
ma-136	205	48	f	f	X
ma-136	205	49	)	)	PUNCT
ma-136	206	1	=	=	NOUN
ma-136	206	2	∞	∞	NOUN
ma-136	206	3	and	and	CCONJ
ma-136	206	4	σ[p+1,q	σ[p+1,q	NOUN
ma-136	206	5	]	]	PUNCT
ma-136	206	6	(	(	PUNCT
ma-136	206	7	f	f	X
ma-136	206	8	)	)	PUNCT
ma-136	206	9	=	=	SYM
ma-136	207	1	σm,[p+1,q	σm,[p+1,q	X
ma-136	207	2	]	]	PUNCT
ma-136	207	3	(	(	PUNCT
ma-136	207	4	f	f	X
ma-136	207	5	)	)	PUNCT
ma-136	207	6	=	=	SYM
ma-136	207	7	µ.	µ.	NOUN
ma-136	207	8	theorem	theorem	VERB
ma-136	207	9	1.4	1.4	NUM
ma-136	207	10	let	let	VERB
ma-136	207	11	p	p	PRON
ma-136	207	12	≥	≥	PRON
ma-136	207	13	q	q	NOUN
ma-136	207	14	≥	≥	NUM
ma-136	207	15	1	1	NUM
ma-136	207	16	be	be	AUX
ma-136	207	17	integers	integer	NOUN
ma-136	207	18	.	.	PUNCT
ma-136	208	1	let	let	VERB
ma-136	208	2	h	h	PRON
ma-136	208	3	be	be	AUX
ma-136	208	4	a	a	DET
ma-136	208	5	set	set	NOUN
ma-136	208	6	of	of	ADP
ma-136	208	7	complex	complex	ADJ
ma-136	208	8	numbers	number	NOUN
ma-136	208	9	satisfying	satisfy	VERB
ma-136	208	10	densd	densd	PROPN
ma-136	208	11	{	{	PUNCT
ma-136	208	12	|z	|z	PROPN
ma-136	209	1	|	|	ADV
ma-136	209	2	:	:	PUNCT
ma-136	209	3	z	z	PROPN
ma-136	209	4	∈	∈	PROPN
ma-136	209	5	h	h	NOUN
ma-136	210	1	⊆	⊆	NUM
ma-136	210	2	d	d	X
ma-136	210	3	}	}	PUNCT
ma-136	210	4	>	>	X
ma-136	210	5	0	0	NUM
ma-136	210	6	,	,	PUNCT
ma-136	210	7	and	and	CCONJ
ma-136	210	8	let	let	VERB
ma-136	210	9	a0	a0	PROPN
ma-136	210	10	,	,	PUNCT
ma-136	210	11	...	...	PUNCT
ma-136	210	12	,	,	PUNCT
ma-136	210	13	ak−1	ak−1	ADV
ma-136	210	14	be	be	AUX
ma-136	210	15	analytic	analytic	ADJ
ma-136	210	16	functions	function	NOUN
ma-136	210	17	in	in	ADP
ma-136	210	18	the	the	DET
ma-136	210	19	unit	unit	NOUN
ma-136	210	20	disc	disc	VERB
ma-136	210	21	d	d	PROPN
ma-136	210	22	such	such	ADJ
ma-136	210	23	that	that	DET
ma-136	210	24	max	max	PROPN
ma-136	210	25	{	{	PUNCT
ma-136	210	26	σm,[p	σm,[p	PROPN
ma-136	210	27	,	,	PUNCT
ma-136	210	28	q	q	X
ma-136	210	29	]	]	X
ma-136	210	30	(	(	PUNCT
ma-136	210	31	ai	ai	PROPN
ma-136	210	32	)	)	PUNCT
ma-136	210	33	:	:	PUNCT
ma-136	211	1	i	i	NOUN
ma-136	211	2	=	=	NOUN
ma-136	211	3	1	1	NUM
ma-136	211	4	,	,	PUNCT
ma-136	211	5	2	2	NUM
ma-136	211	6	,	,	PUNCT
ma-136	211	7	...	...	PUNCT
ma-136	211	8	,	,	PUNCT
ma-136	211	9	k	k	PROPN
ma-136	211	10	−	−	PROPN
ma-136	211	11	1	1	NUM
ma-136	211	12	}	}	PUNCT
ma-136	211	13	≤	≤	NUM
ma-136	211	14	σm,[p	σm,[p	NOUN
ma-136	211	15	,	,	PUNCT
ma-136	211	16	q	q	X
ma-136	211	17	]	]	X
ma-136	211	18	(	(	PUNCT
ma-136	211	19	a0	a0	PROPN
ma-136	211	20	)	)	PUNCT
ma-136	211	21	=	=	SYM
ma-136	211	22	µ	µ	X
ma-136	211	23	(	(	PUNCT
ma-136	211	24	0	0	NUM
ma-136	211	25	<	<	X
ma-136	211	26	µ	µ	X
ma-136	211	27	<	<	X
ma-136	211	28	+	+	NOUN
ma-136	211	29	∞	∞	NOUN
ma-136	211	30	)	)	PUNCT
ma-136	211	31	and	and	CCONJ
ma-136	211	32	if	if	SCONJ
ma-136	211	33	p	p	PROPN
ma-136	211	34	≥	≥	X
ma-136	211	35	q	q	X
ma-136	211	36	≥	≥	NUM
ma-136	211	37	2	2	NUM
ma-136	211	38	,	,	PUNCT
ma-136	211	39	we	we	PRON
ma-136	211	40	have	have	VERB
ma-136	211	41	lim	lim	PROPN
ma-136	211	42	sup	sup	PROPN
ma-136	211	43	|z	|z	PROPN
ma-136	211	44	|→1−,z∈h	|→1−,z∈h	PROPN
ma-136	211	45	logp−1	logp−1	PROPN
ma-136	211	46	t	t	PROPN
ma-136	211	47	(	(	PUNCT
ma-136	211	48	r	r	NOUN
ma-136	211	49	,	,	PUNCT
ma-136	211	50	ai	ai	NOUN
ma-136	211	51	)	)	PUNCT
ma-136	211	52	(	(	PUNCT
ma-136	211	53	logq−1	logq−1	X
ma-136	211	54	(	(	PUNCT
ma-136	211	55	1	1	NUM
ma-136	211	56	1−|z	1−|z	NUM
ma-136	211	57	|	|	NOUN
ma-136	211	58	)	)	PUNCT
ma-136	211	59	)	)	PUNCT
ma-136	211	60	µ	µ	X
ma-136	211	61	<	<	X
ma-136	211	62	lim	lim	PROPN
ma-136	211	63	inf	inf	PROPN
ma-136	211	64	|z	|z	PROPN
ma-136	211	65	|→1−,z∈h	|→1−,z∈h	PROPN
ma-136	211	66	logp−1	logp−1	PROPN
ma-136	211	67	t	t	PROPN
ma-136	211	68	(	(	PUNCT
ma-136	211	69	r	r	PROPN
ma-136	211	70	,	,	PUNCT
ma-136	211	71	a0	a0	NOUN
ma-136	211	72	)	)	PUNCT
ma-136	211	73	(	(	PUNCT
ma-136	211	74	logq−1	logq−1	X
ma-136	211	75	(	(	PUNCT
ma-136	211	76	1	1	NUM
ma-136	211	77	1−|z	1−|z	NUM
ma-136	211	78	|	|	NOUN
ma-136	211	79	)	)	PUNCT
ma-136	211	80	)	)	PUNCT
ma-136	211	81	µ	µ	X
ma-136	211	82	,	,	PUNCT
ma-136	211	83	(	(	PUNCT
ma-136	211	84	i	i	NOUN
ma-136	211	85	=	=	NOUN
ma-136	211	86	1	1	NUM
ma-136	211	87	,	,	PUNCT
ma-136	211	88	...	...	PUNCT
ma-136	211	89	,	,	PUNCT
ma-136	211	90	k	k	PROPN
ma-136	212	1	−	−	PROPN
ma-136	212	2	1	1	NUM
ma-136	212	3	)	)	PUNCT
ma-136	212	4	(	(	PUNCT
ma-136	212	5	1.10	1.10	NUM
ma-136	212	6	)	)	PUNCT
ma-136	212	7	as	as	ADP
ma-136	212	8	|z	|z	PROPN
ma-136	212	9	|	|	ADV
ma-136	212	10	=	=	SYM
ma-136	212	11	r	r	NOUN
ma-136	212	12	→	→	SYM
ma-136	212	13	1−	1−	NUM
ma-136	212	14	for	for	ADP
ma-136	212	15	z	z	PROPN
ma-136	212	16	∈	∈	PROPN
ma-136	212	17	h	h	NOUN
ma-136	212	18	,	,	PUNCT
ma-136	212	19	then	then	ADV
ma-136	212	20	every	every	DET
ma-136	212	21	nontrivial	nontrivial	ADJ
ma-136	212	22	solution	solution	NOUN
ma-136	212	23	f	f	PROPN
ma-136	212	24	of	of	ADP
ma-136	212	25	equation	equation	NOUN
ma-136	212	26	(	(	PUNCT
ma-136	212	27	1.1	1.1	NUM
ma-136	212	28	)	)	PUNCT
ma-136	212	29	satisfies	satisfy	VERB
ma-136	212	30	σ[p	σ[p	NOUN
ma-136	212	31	,	,	PUNCT
ma-136	212	32	q	q	X
ma-136	212	33	]	]	X
ma-136	212	34	(	(	PUNCT
ma-136	212	35	f	f	X
ma-136	212	36	)	)	PUNCT
ma-136	212	37	=	=	SYM
ma-136	213	1	σm,[p	σm,[p	NOUN
ma-136	213	2	,	,	PUNCT
ma-136	213	3	q	q	X
ma-136	213	4	]	]	X
ma-136	213	5	(	(	PUNCT
ma-136	213	6	f	f	X
ma-136	213	7	)	)	PUNCT
ma-136	214	1	=	=	NOUN
ma-136	214	2	∞	∞	NOUN
ma-136	214	3	and	and	CCONJ
ma-136	214	4	σ[p+1,q	σ[p+1,q	NOUN
ma-136	214	5	]	]	PUNCT
ma-136	214	6	(	(	PUNCT
ma-136	214	7	f	f	X
ma-136	214	8	)	)	PUNCT
ma-136	214	9	=	=	SYM
ma-136	215	1	σm,[p+1,q	σm,[p+1,q	X
ma-136	215	2	]	]	PUNCT
ma-136	215	3	(	(	PUNCT
ma-136	215	4	f	f	X
ma-136	215	5	)	)	PUNCT
ma-136	215	6	=	=	PUNCT
ma-136	216	1	µ.	µ.	NOUN
ma-136	216	2	if	if	SCONJ
ma-136	216	3	p	p	NOUN
ma-136	216	4	=	=	X
ma-136	216	5	q	q	NOUN
ma-136	216	6	=	=	NOUN
ma-136	216	7	1	1	NUM
ma-136	216	8	,	,	PUNCT
ma-136	216	9	we	we	PRON
ma-136	216	10	have	have	VERB
ma-136	216	11	lim	lim	PROPN
ma-136	216	12	sup	sup	PROPN
ma-136	216	13	|z	|z	PROPN
ma-136	216	14	|→1−,z∈h	|→1−,z∈h	PROPN
ma-136	216	15	(	(	PUNCT
ma-136	216	16	k	k	PROPN
ma-136	216	17	−	−	PROPN
ma-136	216	18	1)t	1)t	PROPN
ma-136	217	1	(	(	PUNCT
ma-136	217	2	r	r	NOUN
ma-136	217	3	,	,	PUNCT
ma-136	217	4	ai	ai	NOUN
ma-136	217	5	)	)	PUNCT
ma-136	217	6	(	(	PUNCT
ma-136	217	7	1	1	NUM
ma-136	217	8	1−|z	1−|z	NUM
ma-136	217	9	|	|	NOUN
ma-136	217	10	)	)	PUNCT
ma-136	217	11	µ	µ	X
ma-136	217	12	<	<	X
ma-136	217	13	lim	lim	PROPN
ma-136	217	14	inf	inf	PROPN
ma-136	217	15	|z	|z	PROPN
ma-136	217	16	|→1−,z∈h	|→1−,z∈h	PROPN
ma-136	217	17	t	t	PROPN
ma-136	217	18	(	(	PUNCT
ma-136	217	19	r	r	PROPN
ma-136	217	20	,	,	PUNCT
ma-136	217	21	a0	a0	NOUN
ma-136	217	22	)	)	PUNCT
ma-136	217	23	(	(	PUNCT
ma-136	217	24	1	1	NUM
ma-136	217	25	1−|z	1−|z	NUM
ma-136	217	26	|	|	ADJ
ma-136	217	27	)	)	PUNCT
ma-136	217	28	µ	µ	NOUN
ma-136	217	29	,	,	PUNCT
ma-136	217	30	(	(	PUNCT
ma-136	217	31	i	i	NOUN
ma-136	217	32	=	=	NOUN
ma-136	217	33	1	1	NUM
ma-136	217	34	,	,	PUNCT
ma-136	217	35	...	...	PUNCT
ma-136	217	36	,	,	PUNCT
ma-136	218	1	k	k	PROPN
ma-136	219	1	−	−	PROPN
ma-136	219	2	1	1	NUM
ma-136	219	3	)	)	PUNCT
ma-136	219	4	(	(	PUNCT
ma-136	219	5	1.11	1.11	NUM
ma-136	219	6	)	)	PUNCT
ma-136	219	7	as	as	ADP
ma-136	219	8	|z	|z	PROPN
ma-136	219	9	|	|	ADV
ma-136	219	10	=	=	SYM
ma-136	219	11	r	r	NOUN
ma-136	219	12	→	→	SYM
ma-136	219	13	1−	1−	NUM
ma-136	219	14	for	for	ADP
ma-136	219	15	z	z	PROPN
ma-136	219	16	∈	∈	PROPN
ma-136	219	17	h	h	NOUN
ma-136	219	18	,	,	PUNCT
ma-136	219	19	then	then	ADV
ma-136	219	20	every	every	DET
ma-136	219	21	nontrivial	nontrivial	ADJ
ma-136	219	22	solution	solution	NOUN
ma-136	219	23	f	f	PROPN
ma-136	219	24	of	of	ADP
ma-136	219	25	equation	equation	NOUN
ma-136	219	26	(	(	PUNCT
ma-136	219	27	1.1	1.1	NUM
ma-136	219	28	)	)	PUNCT
ma-136	219	29	satisfies	satisfie	NOUN
ma-136	219	30	σ(f	σ(f	ADV
ma-136	219	31	)	)	PUNCT
ma-136	219	32	=	=	SYM
ma-136	219	33	σm(f	σm(f	NOUN
ma-136	219	34	)	)	PUNCT
ma-136	220	1	=	=	SYM
ma-136	220	2	∞	∞	PROPN
ma-136	220	3	and	and	CCONJ
ma-136	220	4	σ2	σ2	PROPN
ma-136	220	5	(	(	PUNCT
ma-136	220	6	f	f	PROPN
ma-136	220	7	)	)	PUNCT
ma-136	221	1	=	=	SYM
ma-136	221	2	σm,2	σm,2	PROPN
ma-136	221	3	(	(	PUNCT
ma-136	221	4	f	f	X
ma-136	221	5	)	)	PUNCT
ma-136	221	6	=	=	SYM
ma-136	221	7	µ.	µ.	NOUN
ma-136	221	8	theorem	theorem	VERB
ma-136	221	9	1.5	1.5	NUM
ma-136	221	10	let	let	VERB
ma-136	221	11	p	p	PRON
ma-136	221	12	≥	≥	PRON
ma-136	221	13	q	q	NOUN
ma-136	221	14	≥	≥	NUM
ma-136	221	15	1	1	NUM
ma-136	221	16	be	be	AUX
ma-136	221	17	integers	integer	NOUN
ma-136	221	18	.	.	PUNCT
ma-136	222	1	let	let	VERB
ma-136	222	2	h	h	PRON
ma-136	222	3	be	be	AUX
ma-136	222	4	a	a	DET
ma-136	222	5	set	set	NOUN
ma-136	222	6	of	of	ADP
ma-136	222	7	complex	complex	ADJ
ma-136	222	8	numbers	number	NOUN
ma-136	222	9	satisfying	satisfy	VERB
ma-136	222	10	densd	densd	PROPN
ma-136	222	11	{	{	PUNCT
ma-136	222	12	|z	|z	PROPN
ma-136	223	1	|	|	ADV
ma-136	223	2	:	:	PUNCT
ma-136	223	3	z	z	PROPN
ma-136	223	4	∈	∈	PROPN
ma-136	223	5	h	h	NOUN
ma-136	224	1	⊆	⊆	NUM
ma-136	224	2	d	d	X
ma-136	224	3	}	}	PUNCT
ma-136	224	4	>	>	X
ma-136	224	5	0	0	NUM
ma-136	224	6	,	,	PUNCT
ma-136	224	7	and	and	CCONJ
ma-136	224	8	let	let	VERB
ma-136	224	9	a0	a0	PROPN
ma-136	224	10	,	,	PUNCT
ma-136	224	11	...	...	PUNCT
ma-136	224	12	,	,	PUNCT
ma-136	224	13	ak	ak	PROPN
ma-136	224	14	be	be	AUX
ma-136	224	15	analytic	analytic	ADJ
ma-136	224	16	functions	function	NOUN
ma-136	224	17	in	in	ADP
ma-136	224	18	the	the	DET
ma-136	224	19	unit	unit	NOUN
ma-136	224	20	disc	disc	VERB
ma-136	224	21	d	d	PROPN
ma-136	224	22	such	such	ADJ
ma-136	224	23	that	that	PRON
ma-136	224	24	for	for	ADP
ma-136	224	25	some	some	DET
ma-136	224	26	constants	constant	NOUN
ma-136	224	27	α	α	DET
ma-136	224	28	≥	≥	NOUN
ma-136	224	29	0	0	NUM
ma-136	224	30	and	and	CCONJ
ma-136	224	31	µ	µ	X
ma-136	224	32	>	>	X
ma-136	224	33	0	0	NUM
ma-136	224	34	,	,	PUNCT
ma-136	224	35	we	we	PRON
ma-136	224	36	have	have	VERB
ma-136	224	37	(	(	PUNCT
ma-136	224	38	1.3	1.3	NUM
ma-136	224	39	)	)	PUNCT
ma-136	224	40	and	and	CCONJ
ma-136	224	41	|ai	|ai	NUM
ma-136	224	42	(	(	PUNCT
ma-136	224	43	z)|	z)|	ADP
ma-136	224	44	≤	≤	NUM
ma-136	224	45	expp	expp	ADJ
ma-136	224	46	{	{	PUNCT
ma-136	224	47	α	α	PROPN
ma-136	224	48	(	(	PUNCT
ma-136	224	49	logq−1	logq−1	X
ma-136	224	50	(	(	PUNCT
ma-136	224	51	1	1	NUM
ma-136	224	52	1−|z	1−|z	NUM
ma-136	224	53	|	|	NOUN
ma-136	224	54	)	)	PUNCT
ma-136	224	55	)	)	PUNCT
ma-136	224	56	µ	µ	X
ma-136	224	57	}	}	PUNCT
ma-136	224	58	,	,	PUNCT
ma-136	224	59	(	(	PUNCT
ma-136	224	60	i	i	NOUN
ma-136	224	61	=	=	NOUN
ma-136	224	62	1	1	NUM
ma-136	224	63	,	,	PUNCT
ma-136	224	64	...	...	PUNCT
ma-136	224	65	,	,	PUNCT
ma-136	224	66	k	k	NOUN
ma-136	224	67	)	)	PUNCT
ma-136	224	68	as	as	ADP
ma-136	224	69	|z	|z	PROPN
ma-136	224	70	|	|	PROPN
ma-136	224	71	→	→	SYM
ma-136	224	72	1−	1−	NUM
ma-136	224	73	for	for	ADP
ma-136	224	74	z	z	PROPN
ma-136	224	75	∈	∈	PROPN
ma-136	224	76	h.	h.	NOUN
ma-136	225	1	then	then	ADV
ma-136	225	2	every	every	DET
ma-136	225	3	meromorphic	meromorphic	ADJ
ma-136	225	4	(	(	PUNCT
ma-136	225	5	or	or	CCONJ
ma-136	225	6	analytic	analytic	ADJ
ma-136	225	7	)	)	PUNCT
ma-136	225	8	solution	solution	NOUN
ma-136	225	9	f	f	PROPN
ma-136	225	10	6≡	6≡	NUM
ma-136	225	11	0	0	NUM
ma-136	225	12	of	of	ADP
ma-136	225	13	equation	equation	NOUN
ma-136	225	14	(	(	PUNCT
ma-136	225	15	1.2	1.2	NUM
ma-136	225	16	)	)	PUNCT
ma-136	225	17	satisfies	satisfy	VERB
ma-136	225	18	σ[p	σ[p	NOUN
ma-136	225	19	,	,	PUNCT
ma-136	225	20	q	q	X
ma-136	225	21	]	]	X
ma-136	225	22	(	(	PUNCT
ma-136	225	23	f	f	X
ma-136	225	24	)	)	PUNCT
ma-136	226	1	=	=	NOUN
ma-136	226	2	∞	∞	NOUN
ma-136	226	3	and	and	CCONJ
ma-136	226	4	σ[p+1,q	σ[p+1,q	NOUN
ma-136	226	5	]	]	PUNCT
ma-136	226	6	(	(	PUNCT
ma-136	226	7	f	f	PROPN
ma-136	226	8	)	)	PUNCT
ma-136	226	9	≥	≥	PROPN
ma-136	226	10	µ.	µ.	PROPN
ma-136	226	11	theorem	theorem	VERB
ma-136	226	12	1.6	1.6	NUM
ma-136	226	13	let	let	VERB
ma-136	226	14	p	p	PRON
ma-136	226	15	≥	≥	PRON
ma-136	226	16	q	q	NOUN
ma-136	226	17	≥	≥	NUM
ma-136	226	18	1	1	NUM
ma-136	226	19	be	be	AUX
ma-136	226	20	integers	integer	NOUN
ma-136	226	21	.	.	PUNCT
ma-136	227	1	let	let	VERB
ma-136	227	2	h	h	PRON
ma-136	227	3	be	be	AUX
ma-136	227	4	a	a	DET
ma-136	227	5	set	set	NOUN
ma-136	227	6	of	of	ADP
ma-136	227	7	complex	complex	ADJ
ma-136	227	8	numbers	number	NOUN
ma-136	227	9	satisfying	satisfy	VERB
ma-136	227	10	densd	densd	PROPN
ma-136	227	11	{	{	PUNCT
ma-136	227	12	|z	|z	PROPN
ma-136	228	1	|	|	ADV
ma-136	228	2	:	:	PUNCT
ma-136	228	3	z	z	PROPN
ma-136	228	4	∈	∈	PROPN
ma-136	228	5	h	h	NOUN
ma-136	229	1	⊆	⊆	NUM
ma-136	229	2	d	d	X
ma-136	229	3	}	}	PUNCT
ma-136	229	4	>	>	X
ma-136	229	5	0	0	NUM
ma-136	229	6	,	,	PUNCT
ma-136	229	7	https://doi.org/10.28924/ada/ma.3.10	https://doi.org/10.28924/ada/ma.3.10	ADV
ma-136	229	8	eur	eur	PROPN
ma-136	229	9	.	.	PUNCT
ma-136	230	1	j.	j.	PROPN
ma-136	230	2	math	math	PROPN
ma-136	230	3	.	.	PUNCT
ma-136	231	1	anal	anal	PROPN
ma-136	231	2	.	.	PUNCT
ma-136	232	1	10.28924	10.28924	NUM
ma-136	232	2	/	/	SYM
ma-136	232	3	ada	ada	NOUN
ma-136	232	4	/	/	NOUN
ma-136	232	5	ma.3.10	ma.3.10	NOUN
ma-136	232	6	9	9	NUM
ma-136	232	7	and	and	CCONJ
ma-136	232	8	let	let	VERB
ma-136	232	9	a0	a0	PROPN
ma-136	232	10	,	,	PUNCT
ma-136	232	11	...	...	PUNCT
ma-136	232	12	,	,	PUNCT
ma-136	232	13	ak	ak	PROPN
ma-136	232	14	be	be	AUX
ma-136	232	15	analytic	analytic	ADJ
ma-136	232	16	functions	function	NOUN
ma-136	232	17	in	in	ADP
ma-136	232	18	the	the	DET
ma-136	232	19	unit	unit	NOUN
ma-136	232	20	disc	disc	VERB
ma-136	232	21	d	d	PROPN
ma-136	232	22	such	such	ADJ
ma-136	232	23	that	that	PRON
ma-136	232	24	for	for	ADP
ma-136	232	25	a	a	DET
ma-136	232	26	constant	constant	ADJ
ma-136	232	27	µ	µ	X
ma-136	232	28	>	>	X
ma-136	232	29	0	0	NUM
ma-136	232	30	,	,	PUNCT
ma-136	232	31	we	we	PRON
ma-136	232	32	have	have	VERB
ma-136	232	33	lim	lim	PROPN
ma-136	232	34	sup	sup	PROPN
ma-136	232	35	|z	|z	PROPN
ma-136	232	36	|→1−,z∈h	|→1−,z∈h	PROPN
ma-136	232	37	logp	logp	NOUN
ma-136	232	38	|ai	|ai	NUM
ma-136	232	39	(	(	PUNCT
ma-136	232	40	z)|	z)|	X
ma-136	232	41	(	(	PUNCT
ma-136	232	42	logq−1	logq−1	X
ma-136	232	43	(	(	PUNCT
ma-136	232	44	1	1	NUM
ma-136	232	45	1−|z	1−|z	NUM
ma-136	232	46	|	|	NOUN
ma-136	232	47	)	)	PUNCT
ma-136	232	48	)	)	PUNCT
ma-136	232	49	µ	µ	X
ma-136	232	50	<	<	X
ma-136	232	51	lim	lim	PROPN
ma-136	232	52	inf	inf	PROPN
ma-136	232	53	|z	|z	PROPN
ma-136	232	54	|→1−,z∈h	|→1−,z∈h	PROPN
ma-136	232	55	logp	logp	NOUN
ma-136	233	1	|a0	|a0	PROPN
ma-136	233	2	(	(	PUNCT
ma-136	233	3	z)|	z)|	X
ma-136	233	4	(	(	PUNCT
ma-136	233	5	logq−1	logq−1	X
ma-136	233	6	(	(	PUNCT
ma-136	233	7	1	1	NUM
ma-136	233	8	1−|z	1−|z	NUM
ma-136	233	9	|	|	NOUN
ma-136	233	10	)	)	PUNCT
ma-136	233	11	)	)	PUNCT
ma-136	233	12	µ	µ	X
ma-136	233	13	,	,	PUNCT
ma-136	233	14	(	(	PUNCT
ma-136	233	15	i	i	NOUN
ma-136	233	16	=	=	NOUN
ma-136	233	17	1	1	NUM
ma-136	233	18	,	,	PUNCT
ma-136	233	19	...	...	PUNCT
ma-136	233	20	,	,	PUNCT
ma-136	233	21	k	k	NOUN
ma-136	233	22	)	)	PUNCT
ma-136	233	23	as	as	ADP
ma-136	233	24	|z	|z	PROPN
ma-136	233	25	|	|	PROPN
ma-136	233	26	→	→	SYM
ma-136	233	27	1−	1−	NUM
ma-136	233	28	for	for	ADP
ma-136	233	29	z	z	PROPN
ma-136	233	30	∈	∈	PROPN
ma-136	233	31	h.then	h.then	ADP
ma-136	233	32	every	every	DET
ma-136	233	33	meromorphic	meromorphic	ADJ
ma-136	233	34	(	(	PUNCT
ma-136	233	35	or	or	CCONJ
ma-136	233	36	analytic	analytic	ADJ
ma-136	233	37	)	)	PUNCT
ma-136	233	38	solution	solution	NOUN
ma-136	233	39	f	f	PROPN
ma-136	233	40	6≡	6≡	NUM
ma-136	233	41	0	0	NUM
ma-136	233	42	of	of	ADP
ma-136	233	43	equation	equation	NOUN
ma-136	233	44	(	(	PUNCT
ma-136	233	45	1.2	1.2	NUM
ma-136	233	46	)	)	PUNCT
ma-136	233	47	satisfies	satisfy	VERB
ma-136	233	48	σ[p	σ[p	NOUN
ma-136	233	49	,	,	PUNCT
ma-136	233	50	q	q	X
ma-136	233	51	]	]	X
ma-136	233	52	(	(	PUNCT
ma-136	233	53	f	f	X
ma-136	233	54	)	)	PUNCT
ma-136	234	1	=	=	NOUN
ma-136	234	2	∞	∞	NOUN
ma-136	234	3	and	and	CCONJ
ma-136	234	4	σ[p+1,q	σ[p+1,q	NOUN
ma-136	234	5	]	]	PUNCT
ma-136	234	6	(	(	PUNCT
ma-136	234	7	f	f	PROPN
ma-136	234	8	)	)	PUNCT
ma-136	234	9	≥	≥	PROPN
ma-136	234	10	µ.	µ.	PROPN
ma-136	234	11	theorem	theorem	VERB
ma-136	234	12	1.7	1.7	NUM
ma-136	234	13	let	let	VERB
ma-136	234	14	p	p	PRON
ma-136	234	15	≥	≥	PRON
ma-136	234	16	q	q	NOUN
ma-136	234	17	≥	≥	NUM
ma-136	234	18	1	1	NUM
ma-136	234	19	be	be	AUX
ma-136	234	20	integers	integer	NOUN
ma-136	234	21	.	.	PUNCT
ma-136	235	1	let	let	VERB
ma-136	235	2	h	h	PRON
ma-136	235	3	be	be	AUX
ma-136	235	4	a	a	DET
ma-136	235	5	set	set	NOUN
ma-136	235	6	of	of	ADP
ma-136	235	7	complex	complex	ADJ
ma-136	235	8	numbers	number	NOUN
ma-136	235	9	satisfying	satisfy	VERB
ma-136	235	10	densd	densd	PROPN
ma-136	235	11	{	{	PUNCT
ma-136	235	12	|z	|z	PROPN
ma-136	236	1	|	|	ADV
ma-136	236	2	:	:	PUNCT
ma-136	236	3	z	z	PROPN
ma-136	236	4	∈	∈	PROPN
ma-136	236	5	h	h	NOUN
ma-136	237	1	⊆	⊆	NUM
ma-136	237	2	d	d	X
ma-136	237	3	}	}	PUNCT
ma-136	237	4	>	>	X
ma-136	237	5	0	0	NUM
ma-136	237	6	,	,	PUNCT
ma-136	237	7	and	and	CCONJ
ma-136	237	8	let	let	VERB
ma-136	237	9	a0	a0	PROPN
ma-136	237	10	,	,	PUNCT
ma-136	237	11	...	...	PUNCT
ma-136	237	12	,	,	PUNCT
ma-136	237	13	ak	ak	PROPN
ma-136	237	14	be	be	AUX
ma-136	237	15	analytic	analytic	ADJ
ma-136	237	16	functions	function	NOUN
ma-136	237	17	in	in	ADP
ma-136	237	18	the	the	DET
ma-136	237	19	unit	unit	NOUN
ma-136	237	20	disc	disc	VERB
ma-136	237	21	d	d	PROPN
ma-136	237	22	such	such	ADJ
ma-136	237	23	that	that	PRON
ma-136	237	24	for	for	ADP
ma-136	237	25	some	some	DET
ma-136	237	26	constants	constant	NOUN
ma-136	237	27	α	α	DET
ma-136	237	28	≥	≥	NOUN
ma-136	237	29	0	0	NUM
ma-136	237	30	and	and	CCONJ
ma-136	237	31	µ	µ	X
ma-136	237	32	>	>	X
ma-136	237	33	0	0	NUM
ma-136	237	34	,	,	PUNCT
ma-136	237	35	if	if	SCONJ
ma-136	237	36	p	p	PROPN
ma-136	237	37	≥	≥	PUNCT
ma-136	237	38	q	q	X
ma-136	237	39	≥	≥	NUM
ma-136	237	40	2	2	NUM
ma-136	237	41	we	we	PRON
ma-136	237	42	have	have	VERB
ma-136	237	43	lim	lim	PROPN
ma-136	237	44	inf	inf	PROPN
ma-136	237	45	|z	|z	PROPN
ma-136	237	46	|→1−,z∈h	|→1−,z∈h	PROPN
ma-136	237	47	logp−1	logp−1	PROPN
ma-136	237	48	t	t	PROPN
ma-136	237	49	(	(	PUNCT
ma-136	237	50	r	r	PROPN
ma-136	237	51	,	,	PUNCT
ma-136	237	52	a0	a0	NOUN
ma-136	237	53	)	)	PUNCT
ma-136	237	54	(	(	PUNCT
ma-136	237	55	logq−1	logq−1	X
ma-136	237	56	(	(	PUNCT
ma-136	237	57	1	1	NUM
ma-136	237	58	1−|z	1−|z	NUM
ma-136	237	59	|	|	NOUN
ma-136	237	60	)	)	PUNCT
ma-136	237	61	)	)	PUNCT
ma-136	237	62	µ	µ	X
ma-136	237	63	>	>	X
ma-136	237	64	α	α	PROPN
ma-136	237	65	(	(	PUNCT
ma-136	237	66	1.12	1.12	NUM
ma-136	237	67	)	)	PUNCT
ma-136	237	68	and	and	CCONJ
ma-136	237	69	t	t	PROPN
ma-136	237	70	(	(	PUNCT
ma-136	237	71	r	r	NOUN
ma-136	237	72	,	,	PUNCT
ma-136	237	73	ai	ai	NOUN
ma-136	237	74	)	)	PUNCT
ma-136	237	75	≤	≤	NOUN
ma-136	237	76	expp−1	expp−1	PROPN
ma-136	237	77	{	{	PUNCT
ma-136	237	78	α	α	PROPN
ma-136	237	79	(	(	PUNCT
ma-136	237	80	logq−1	logq−1	X
ma-136	237	81	(	(	PUNCT
ma-136	237	82	1	1	NUM
ma-136	237	83	1−|z	1−|z	NUM
ma-136	237	84	|	|	NOUN
ma-136	237	85	)	)	PUNCT
ma-136	237	86	)	)	PUNCT
ma-136	237	87	µ	µ	X
ma-136	237	88	}	}	PUNCT
ma-136	237	89	,	,	PUNCT
ma-136	237	90	(	(	PUNCT
ma-136	237	91	i	i	NOUN
ma-136	237	92	=	=	NOUN
ma-136	237	93	1	1	NUM
ma-136	237	94	,	,	PUNCT
ma-136	237	95	...	...	PUNCT
ma-136	237	96	,	,	PUNCT
ma-136	237	97	k	k	X
ma-136	237	98	)	)	PUNCT
ma-136	237	99	(	(	PUNCT
ma-136	237	100	1.13	1.13	NUM
ma-136	237	101	)	)	PUNCT
ma-136	237	102	as	as	ADP
ma-136	237	103	|z	|z	PROPN
ma-136	237	104	|	|	ADV
ma-136	237	105	=	=	SYM
ma-136	237	106	r	r	NOUN
ma-136	237	107	→	→	SYM
ma-136	237	108	1−	1−	NUM
ma-136	237	109	for	for	ADP
ma-136	237	110	z	z	PROPN
ma-136	237	111	∈	∈	PROPN
ma-136	237	112	h	h	NOUN
ma-136	237	113	,	,	PUNCT
ma-136	237	114	then	then	ADV
ma-136	237	115	every	every	DET
ma-136	237	116	meromorphic	meromorphic	ADJ
ma-136	237	117	(	(	PUNCT
ma-136	237	118	or	or	CCONJ
ma-136	237	119	analytic	analytic	ADJ
ma-136	237	120	)	)	PUNCT
ma-136	237	121	solution	solution	NOUN
ma-136	237	122	f	f	PROPN
ma-136	237	123	6≡	6≡	NUM
ma-136	237	124	0	0	NUM
ma-136	237	125	of	of	ADP
ma-136	237	126	equation	equation	NOUN
ma-136	237	127	(	(	PUNCT
ma-136	237	128	1.2	1.2	NUM
ma-136	237	129	)	)	PUNCT
ma-136	237	130	satisfies	satisfy	VERB
ma-136	237	131	σ[p	σ[p	NOUN
ma-136	237	132	,	,	PUNCT
ma-136	237	133	q	q	X
ma-136	237	134	]	]	X
ma-136	237	135	(	(	PUNCT
ma-136	237	136	f	f	X
ma-136	237	137	)	)	PUNCT
ma-136	238	1	=	=	NOUN
ma-136	238	2	∞	∞	NOUN
ma-136	238	3	and	and	CCONJ
ma-136	238	4	σ[p+1,q	σ[p+1,q	NOUN
ma-136	238	5	]	]	PUNCT
ma-136	238	6	(	(	PUNCT
ma-136	238	7	f	f	PROPN
ma-136	238	8	)	)	PUNCT
ma-136	238	9	≥	≥	PROPN
ma-136	238	10	µ.	µ.	NOUN
ma-136	239	1	if	if	SCONJ
ma-136	239	2	p	p	NOUN
ma-136	239	3	=	=	X
ma-136	239	4	q	q	NOUN
ma-136	239	5	=	=	NOUN
ma-136	239	6	1	1	NUM
ma-136	239	7	,	,	PUNCT
ma-136	239	8	we	we	PRON
ma-136	239	9	have	have	VERB
ma-136	239	10	lim	lim	PROPN
ma-136	239	11	inf	inf	PROPN
ma-136	240	1	|z	|z	PROPN
ma-136	240	2	|→1−,z∈h	|→1−,z∈h	PROPN
ma-136	240	3	t	t	PROPN
ma-136	240	4	(	(	PUNCT
ma-136	240	5	r	r	PROPN
ma-136	240	6	,	,	PUNCT
ma-136	240	7	a0	a0	NOUN
ma-136	240	8	)	)	PUNCT
ma-136	240	9	(	(	PUNCT
ma-136	240	10	1	1	NUM
ma-136	240	11	1−|z	1−|z	NUM
ma-136	240	12	|	|	NOUN
ma-136	240	13	)	)	PUNCT
ma-136	241	1	µ	µ	X
ma-136	241	2	>	>	X
ma-136	241	3	kα	kα	PROPN
ma-136	241	4	(	(	PUNCT
ma-136	241	5	1.14	1.14	NUM
ma-136	241	6	)	)	PUNCT
ma-136	241	7	and	and	CCONJ
ma-136	241	8	t	t	PROPN
ma-136	241	9	(	(	PUNCT
ma-136	241	10	r	r	NOUN
ma-136	241	11	,	,	PUNCT
ma-136	241	12	ai	ai	NOUN
ma-136	241	13	)	)	PUNCT
ma-136	241	14	≤	≤	NOUN
ma-136	241	15	α	α	PROPN
ma-136	241	16	(	(	PUNCT
ma-136	241	17	1	1	NUM
ma-136	241	18	1−|z	1−|z	NUM
ma-136	241	19	|	|	ADJ
ma-136	241	20	)	)	PUNCT
ma-136	241	21	µ	µ	NOUN
ma-136	241	22	,	,	PUNCT
ma-136	241	23	(	(	PUNCT
ma-136	241	24	i	i	NOUN
ma-136	241	25	=	=	NOUN
ma-136	241	26	1	1	NUM
ma-136	241	27	,	,	PUNCT
ma-136	241	28	...	...	PUNCT
ma-136	241	29	,	,	PUNCT
ma-136	241	30	k	k	X
ma-136	241	31	)	)	PUNCT
ma-136	241	32	(	(	PUNCT
ma-136	241	33	1.15	1.15	NUM
ma-136	241	34	)	)	PUNCT
ma-136	241	35	as	as	ADP
ma-136	241	36	|z	|z	PROPN
ma-136	241	37	|	|	ADV
ma-136	241	38	=	=	SYM
ma-136	241	39	r	r	NOUN
ma-136	241	40	→	→	SYM
ma-136	241	41	1−	1−	NUM
ma-136	241	42	for	for	ADP
ma-136	241	43	z	z	PROPN
ma-136	241	44	∈	∈	PROPN
ma-136	241	45	h	h	NOUN
ma-136	241	46	,	,	PUNCT
ma-136	241	47	then	then	ADV
ma-136	241	48	every	every	DET
ma-136	241	49	meromorphic	meromorphic	ADJ
ma-136	241	50	(	(	PUNCT
ma-136	241	51	or	or	CCONJ
ma-136	241	52	analytic	analytic	ADJ
ma-136	241	53	)	)	PUNCT
ma-136	241	54	solution	solution	NOUN
ma-136	241	55	f	f	PROPN
ma-136	241	56	6≡	6≡	NUM
ma-136	241	57	0	0	NUM
ma-136	241	58	of	of	ADP
ma-136	241	59	equation	equation	NOUN
ma-136	241	60	(	(	PUNCT
ma-136	241	61	1.2	1.2	NUM
ma-136	241	62	)	)	PUNCT
ma-136	241	63	satisfies	satisfie	NOUN
ma-136	241	64	σ	σ	X
ma-136	241	65	(	(	PUNCT
ma-136	241	66	f	f	PROPN
ma-136	241	67	)	)	PUNCT
ma-136	242	1	=	=	NOUN
ma-136	242	2	∞	∞	PROPN
ma-136	242	3	and	and	CCONJ
ma-136	242	4	σ2	σ2	PROPN
ma-136	242	5	(	(	PUNCT
ma-136	242	6	f	f	PROPN
ma-136	242	7	)	)	PUNCT
ma-136	242	8	≥	≥	PROPN
ma-136	242	9	µ.	µ.	PROPN
ma-136	242	10	theorem	theorem	VERB
ma-136	242	11	1.8	1.8	NUM
ma-136	242	12	let	let	VERB
ma-136	242	13	p	p	PRON
ma-136	242	14	≥	≥	PRON
ma-136	242	15	q	q	NOUN
ma-136	242	16	≥	≥	NUM
ma-136	242	17	1	1	NUM
ma-136	242	18	be	be	AUX
ma-136	242	19	integers	integer	NOUN
ma-136	242	20	.	.	PUNCT
ma-136	243	1	let	let	VERB
ma-136	243	2	h	h	PRON
ma-136	243	3	be	be	AUX
ma-136	243	4	a	a	DET
ma-136	243	5	set	set	NOUN
ma-136	243	6	of	of	ADP
ma-136	243	7	complex	complex	ADJ
ma-136	243	8	numbers	number	NOUN
ma-136	243	9	satisfying	satisfy	VERB
ma-136	243	10	densd	densd	PROPN
ma-136	243	11	{	{	PUNCT
ma-136	243	12	|z	|z	PROPN
ma-136	244	1	|	|	ADV
ma-136	244	2	:	:	PUNCT
ma-136	244	3	z	z	PROPN
ma-136	244	4	∈	∈	PROPN
ma-136	244	5	h	h	NOUN
ma-136	245	1	⊆	⊆	NUM
ma-136	245	2	d	d	X
ma-136	245	3	}	}	PUNCT
ma-136	245	4	>	>	X
ma-136	245	5	0	0	NUM
ma-136	245	6	,	,	PUNCT
ma-136	245	7	and	and	CCONJ
ma-136	245	8	let	let	VERB
ma-136	245	9	a0	a0	PROPN
ma-136	245	10	(	(	PUNCT
ma-136	245	11	z	z	NOUN
ma-136	245	12	)	)	PUNCT
ma-136	245	13	,	,	PUNCT
ma-136	245	14	...	...	PUNCT
ma-136	245	15	,	,	PUNCT
ma-136	245	16	ak	ak	PROPN
ma-136	245	17	(	(	PUNCT
ma-136	245	18	z	z	NOUN
ma-136	245	19	)	)	PUNCT
ma-136	245	20	be	be	AUX
ma-136	245	21	analytic	analytic	ADJ
ma-136	245	22	functions	function	NOUN
ma-136	245	23	in	in	ADP
ma-136	245	24	the	the	DET
ma-136	245	25	unit	unit	NOUN
ma-136	245	26	disc	disc	VERB
ma-136	245	27	d	d	PROPN
ma-136	245	28	such	such	ADJ
ma-136	245	29	that	that	PRON
ma-136	245	30	for	for	ADP
ma-136	245	31	a	a	DET
ma-136	245	32	constant	constant	ADJ
ma-136	245	33	µ	µ	X
ma-136	245	34	>	>	X
ma-136	245	35	0	0	NUM
ma-136	245	36	,	,	PUNCT
ma-136	245	37	if	if	SCONJ
ma-136	245	38	p	p	PROPN
ma-136	245	39	≥	≥	PUNCT
ma-136	245	40	q	q	X
ma-136	245	41	≥	≥	NUM
ma-136	245	42	2	2	NUM
ma-136	245	43	we	we	PRON
ma-136	245	44	have	have	AUX
ma-136	245	45	lim	lim	PROPN
ma-136	245	46	sup	sup	PROPN
ma-136	245	47	|z	|z	PROPN
ma-136	245	48	|→1−,z∈h	|→1−,z∈h	PROPN
ma-136	245	49	logp−1	logp−1	PROPN
ma-136	245	50	t	t	PROPN
ma-136	245	51	(	(	PUNCT
ma-136	245	52	r	r	NOUN
ma-136	245	53	,	,	PUNCT
ma-136	245	54	ai	ai	NOUN
ma-136	245	55	)	)	PUNCT
ma-136	245	56	(	(	PUNCT
ma-136	245	57	logq−1	logq−1	X
ma-136	245	58	(	(	PUNCT
ma-136	245	59	1	1	NUM
ma-136	245	60	1−|z	1−|z	NUM
ma-136	245	61	|	|	NOUN
ma-136	245	62	)	)	PUNCT
ma-136	245	63	)	)	PUNCT
ma-136	245	64	µ	µ	X
ma-136	245	65	<	<	X
ma-136	245	66	lim	lim	PROPN
ma-136	245	67	inf	inf	PROPN
ma-136	245	68	|z	|z	PROPN
ma-136	245	69	|→1−,z∈h	|→1−,z∈h	PROPN
ma-136	245	70	logp−1	logp−1	PROPN
ma-136	245	71	t	t	PROPN
ma-136	245	72	(	(	PUNCT
ma-136	245	73	r	r	PROPN
ma-136	245	74	,	,	PUNCT
ma-136	245	75	a0	a0	NOUN
ma-136	245	76	)	)	PUNCT
ma-136	245	77	(	(	PUNCT
ma-136	245	78	logq−1	logq−1	X
ma-136	245	79	(	(	PUNCT
ma-136	245	80	1	1	NUM
ma-136	245	81	1−|z	1−|z	NUM
ma-136	245	82	|	|	NOUN
ma-136	245	83	)	)	PUNCT
ma-136	245	84	)	)	PUNCT
ma-136	245	85	µ	µ	X
ma-136	245	86	,	,	PUNCT
ma-136	245	87	(	(	PUNCT
ma-136	245	88	i	i	NOUN
ma-136	245	89	=	=	NOUN
ma-136	245	90	1	1	NUM
ma-136	245	91	,	,	PUNCT
ma-136	245	92	...	...	PUNCT
ma-136	245	93	,	,	PUNCT
ma-136	245	94	k	k	X
ma-136	245	95	)	)	PUNCT
ma-136	245	96	(	(	PUNCT
ma-136	245	97	1.16	1.16	NUM
ma-136	245	98	)	)	PUNCT
ma-136	245	99	https://doi.org/10.28924/ada/ma.3.10	https://doi.org/10.28924/ada/ma.3.10	ADV
ma-136	245	100	eur	eur	PROPN
ma-136	245	101	.	.	PUNCT
ma-136	246	1	j.	j.	PROPN
ma-136	246	2	math	math	PROPN
ma-136	246	3	.	.	PUNCT
ma-136	247	1	anal	anal	PROPN
ma-136	247	2	.	.	PUNCT
ma-136	248	1	10.28924	10.28924	NUM
ma-136	248	2	/	/	SYM
ma-136	248	3	ada	ada	NOUN
ma-136	248	4	/	/	NOUN
ma-136	248	5	ma.3.10	ma.3.10	ADJ
ma-136	248	6	10	10	NUM
ma-136	248	7	as	as	ADP
ma-136	248	8	|z	|z	PROPN
ma-136	248	9	|	|	ADV
ma-136	248	10	=	=	SYM
ma-136	248	11	r	r	NOUN
ma-136	248	12	→	→	SYM
ma-136	248	13	1−	1−	NUM
ma-136	248	14	for	for	ADP
ma-136	248	15	z	z	PROPN
ma-136	248	16	∈	∈	PROPN
ma-136	248	17	h	h	NOUN
ma-136	248	18	,	,	PUNCT
ma-136	248	19	then	then	ADV
ma-136	248	20	every	every	DET
ma-136	248	21	meromorphic	meromorphic	ADJ
ma-136	248	22	(	(	PUNCT
ma-136	248	23	or	or	CCONJ
ma-136	248	24	analytic	analytic	ADJ
ma-136	248	25	)	)	PUNCT
ma-136	248	26	solution	solution	NOUN
ma-136	248	27	f	f	PROPN
ma-136	248	28	6≡	6≡	NUM
ma-136	248	29	0	0	NUM
ma-136	248	30	of	of	ADP
ma-136	248	31	equation	equation	NOUN
ma-136	248	32	(	(	PUNCT
ma-136	248	33	1.2	1.2	NUM
ma-136	248	34	)	)	PUNCT
ma-136	248	35	satisfies	satisfy	VERB
ma-136	248	36	σ[p	σ[p	NOUN
ma-136	248	37	,	,	PUNCT
ma-136	248	38	q	q	X
ma-136	248	39	]	]	X
ma-136	248	40	(	(	PUNCT
ma-136	248	41	f	f	X
ma-136	248	42	)	)	PUNCT
ma-136	249	1	=	=	NOUN
ma-136	249	2	∞	∞	NOUN
ma-136	249	3	and	and	CCONJ
ma-136	249	4	σ[p+1,q	σ[p+1,q	NOUN
ma-136	249	5	]	]	PUNCT
ma-136	249	6	(	(	PUNCT
ma-136	249	7	f	f	PROPN
ma-136	249	8	)	)	PUNCT
ma-136	249	9	≥	≥	PROPN
ma-136	249	10	µ.	µ.	NOUN
ma-136	250	1	if	if	SCONJ
ma-136	250	2	p	p	NOUN
ma-136	250	3	=	=	X
ma-136	250	4	q	q	NOUN
ma-136	250	5	=	=	NOUN
ma-136	250	6	1	1	NUM
ma-136	250	7	,	,	PUNCT
ma-136	250	8	we	we	PRON
ma-136	250	9	have	have	VERB
ma-136	250	10	lim	lim	PROPN
ma-136	250	11	sup	sup	PROPN
ma-136	250	12	|z	|z	PROPN
ma-136	250	13	|→1−,z∈h	|→1−,z∈h	PROPN
ma-136	250	14	kt	kt	PROPN
ma-136	250	15	(	(	PUNCT
ma-136	250	16	|z	|z	PROPN
ma-136	251	1	|	|	ADV
ma-136	251	2	,	,	PUNCT
ma-136	251	3	ai	ai	VERB
ma-136	251	4	)	)	PUNCT
ma-136	251	5	(	(	PUNCT
ma-136	251	6	1	1	NUM
ma-136	251	7	1−|z	1−|z	NUM
ma-136	251	8	|	|	NOUN
ma-136	251	9	)	)	PUNCT
ma-136	252	1	µ	µ	X
ma-136	252	2	<	<	X
ma-136	252	3	lim	lim	PROPN
ma-136	252	4	inf	inf	PROPN
ma-136	252	5	|z	|z	PROPN
ma-136	252	6	|→1−,z∈h	|→1−,z∈h	PROPN
ma-136	252	7	t	t	PROPN
ma-136	252	8	(	(	PUNCT
ma-136	252	9	|z	|z	PROPN
ma-136	253	1	|	|	ADV
ma-136	253	2	,	,	PUNCT
ma-136	253	3	a0	a0	PROPN
ma-136	253	4	)	)	PUNCT
ma-136	253	5	(	(	PUNCT
ma-136	253	6	1	1	NUM
ma-136	253	7	1−|z	1−|z	NUM
ma-136	253	8	|	|	ADJ
ma-136	253	9	)	)	PUNCT
ma-136	253	10	µ	µ	NOUN
ma-136	253	11	,	,	PUNCT
ma-136	253	12	(	(	PUNCT
ma-136	253	13	i	i	NOUN
ma-136	253	14	=	=	NOUN
ma-136	253	15	1	1	NUM
ma-136	253	16	,	,	PUNCT
ma-136	253	17	...	...	PUNCT
ma-136	253	18	,	,	PUNCT
ma-136	253	19	k	k	X
ma-136	253	20	)	)	PUNCT
ma-136	253	21	(	(	PUNCT
ma-136	253	22	1.17	1.17	NUM
ma-136	253	23	)	)	PUNCT
ma-136	253	24	as	as	ADP
ma-136	253	25	|z	|z	PROPN
ma-136	253	26	|	|	ADV
ma-136	253	27	=	=	SYM
ma-136	253	28	r	r	NOUN
ma-136	253	29	→	→	SYM
ma-136	253	30	1−	1−	NUM
ma-136	253	31	for	for	ADP
ma-136	253	32	z	z	PROPN
ma-136	253	33	∈	∈	PROPN
ma-136	253	34	h	h	NOUN
ma-136	253	35	,	,	PUNCT
ma-136	253	36	then	then	ADV
ma-136	253	37	every	every	DET
ma-136	253	38	meromorphic	meromorphic	ADJ
ma-136	253	39	(	(	PUNCT
ma-136	253	40	or	or	CCONJ
ma-136	253	41	analytic	analytic	ADJ
ma-136	253	42	)	)	PUNCT
ma-136	253	43	solution	solution	NOUN
ma-136	253	44	f	f	PROPN
ma-136	253	45	6≡	6≡	NUM
ma-136	253	46	0	0	NUM
ma-136	253	47	of	of	ADP
ma-136	253	48	equation	equation	NOUN
ma-136	253	49	(	(	PUNCT
ma-136	253	50	1.2	1.2	NUM
ma-136	253	51	)	)	PUNCT
ma-136	253	52	satisfies	satisfie	NOUN
ma-136	253	53	σ(f	σ(f	ADV
ma-136	253	54	)	)	PUNCT
ma-136	254	1	=	=	PUNCT
ma-136	254	2	∞	∞	PROPN
ma-136	254	3	and	and	CCONJ
ma-136	254	4	σ2	σ2	PROPN
ma-136	254	5	(	(	PUNCT
ma-136	254	6	f	f	PROPN
ma-136	254	7	)	)	PUNCT
ma-136	254	8	≥	≥	PROPN
ma-136	254	9	µ.	µ.	NOUN
ma-136	254	10	remark	remark	VERB
ma-136	254	11	1.2	1.2	NUM
ma-136	254	12	for	for	ADP
ma-136	254	13	equation	equation	NOUN
ma-136	254	14	(	(	PUNCT
ma-136	254	15	1.1	1.1	NUM
ma-136	254	16	)	)	PUNCT
ma-136	254	17	,	,	PUNCT
ma-136	254	18	we	we	PRON
ma-136	254	19	can	can	AUX
ma-136	254	20	easily	easily	ADV
ma-136	254	21	conclude	conclude	VERB
ma-136	254	22	that	that	SCONJ
ma-136	254	23	theorems	theorem	VERB
ma-136	254	24	a	a	PRON
ma-136	254	25	-	-	PUNCT
ma-136	254	26	c	c	NOUN
ma-136	254	27	are	be	AUX
ma-136	254	28	generalized	generalized	ADJ
ma-136	254	29	totheorems	totheorem	NOUN
ma-136	254	30	1.1	1.1	NUM
ma-136	254	31	-	-	SYM
ma-136	254	32	1.4	1.4	NUM
ma-136	254	33	.	.	PUNCT
ma-136	255	1	in	in	ADP
ma-136	255	2	the	the	DET
ma-136	255	3	same	same	ADJ
ma-136	255	4	paper	paper	NOUN
ma-136	255	5	,	,	PUNCT
ma-136	255	6	chen	chen	PROPN
ma-136	255	7	et	et	PROPN
ma-136	255	8	al	al	PROPN
ma-136	255	9	.	.	PUNCT
ma-136	256	1	[	[	X
ma-136	256	2	9	9	NUM
ma-136	256	3	]	]	PUNCT
ma-136	256	4	obtained	obtain	VERB
ma-136	256	5	some	some	DET
ma-136	256	6	results	result	NOUN
ma-136	256	7	of	of	ADP
ma-136	256	8	the	the	DET
ma-136	256	9	fixed	fix	VERB
ma-136	256	10	points	point	NOUN
ma-136	256	11	of	of	ADP
ma-136	256	12	solutions	solution	NOUN
ma-136	256	13	andtheir	andtheir	VERB
ma-136	256	14	arbitrary	arbitrary	ADJ
ma-136	256	15	order	order	NOUN
ma-136	256	16	derivatives	derivative	NOUN
ma-136	256	17	of	of	ADP
ma-136	256	18	equations	equation	NOUN
ma-136	256	19	(	(	PUNCT
ma-136	256	20	1.1	1.1	NUM
ma-136	256	21	)	)	PUNCT
ma-136	256	22	and	and	CCONJ
ma-136	256	23	(	(	PUNCT
ma-136	256	24	1.2	1.2	NUM
ma-136	256	25	)	)	PUNCT
ma-136	256	26	.	.	PUNCT
ma-136	257	1	here	here	ADV
ma-136	257	2	,	,	PUNCT
ma-136	257	3	we	we	PRON
ma-136	257	4	generalize	generalize	VERB
ma-136	257	5	these	these	DET
ma-136	257	6	results	result	NOUN
ma-136	257	7	,	,	PUNCT
ma-136	257	8	and	and	CCONJ
ma-136	257	9	we	we	PRON
ma-136	257	10	obtain	obtain	VERB
ma-136	257	11	our	our	PRON
ma-136	257	12	theorems	theorem	NOUN
ma-136	257	13	as	as	ADP
ma-136	257	14	following	follow	VERB
ma-136	257	15	.	.	PUNCT
ma-136	258	1	theorem	theorem	VERB
ma-136	258	2	1.9	1.9	NUM
ma-136	258	3	assume	assume	VERB
ma-136	258	4	that	that	SCONJ
ma-136	258	5	the	the	DET
ma-136	258	6	assumptions	assumption	NOUN
ma-136	258	7	of	of	ADP
ma-136	258	8	theorem	theorem	ADJ
ma-136	258	9	1.1	1.1	NUM
ma-136	258	10	or	or	CCONJ
ma-136	258	11	theorem	theorem	VERB
ma-136	258	12	1.2	1.2	NUM
ma-136	258	13	hold	hold	NOUN
ma-136	258	14	.	.	PUNCT
ma-136	259	1	then	then	ADV
ma-136	259	2	every	every	DET
ma-136	259	3	solution	solution	NOUN
ma-136	259	4	f	f	PROPN
ma-136	259	5	6≡	6≡	NUM
ma-136	259	6	0	0	NUM
ma-136	259	7	of	of	ADP
ma-136	259	8	equation	equation	NOUN
ma-136	259	9	(	(	PUNCT
ma-136	259	10	1.1	1.1	NUM
ma-136	259	11	)	)	PUNCT
ma-136	259	12	satisfies	satisfie	NOUN
ma-136	259	13	λ̄[p	λ̄[p	PROPN
ma-136	259	14	,	,	PUNCT
ma-136	259	15	q	q	X
ma-136	259	16	]	]	X
ma-136	259	17	(	(	PUNCT
ma-136	259	18	f	f	X
ma-136	259	19	(	(	PUNCT
ma-136	259	20	j	j	PROPN
ma-136	259	21	)	)	PUNCT
ma-136	259	22	−	−	PROPN
ma-136	259	23	z	z	NOUN
ma-136	259	24	)	)	PUNCT
ma-136	260	1	=	=	SYM
ma-136	260	2	λ[p	λ[p	NUM
ma-136	260	3	,	,	PUNCT
ma-136	260	4	q	q	X
ma-136	260	5	]	]	X
ma-136	260	6	(	(	PUNCT
ma-136	260	7	f	f	PROPN
ma-136	260	8	−	−	PROPN
ma-136	260	9	z	z	PROPN
ma-136	260	10	)	)	PUNCT
ma-136	260	11	=	=	SYM
ma-136	260	12	σ[p	σ[p	NOUN
ma-136	260	13	,	,	PUNCT
ma-136	260	14	q	q	X
ma-136	260	15	]	]	X
ma-136	260	16	(	(	PUNCT
ma-136	260	17	f	f	X
ma-136	260	18	)	)	PUNCT
ma-136	260	19	=	=	NOUN
ma-136	260	20	∞	∞	NOUN
ma-136	260	21	,	,	PUNCT
ma-136	260	22	λ̄[p+1,q	λ̄[p+1,q	NOUN
ma-136	260	23	]	]	X
ma-136	260	24	(	(	PUNCT
ma-136	260	25	f	f	X
ma-136	260	26	(	(	PUNCT
ma-136	260	27	j	j	PROPN
ma-136	260	28	)	)	PUNCT
ma-136	260	29	−	−	PROPN
ma-136	260	30	z	z	NOUN
ma-136	260	31	)	)	PUNCT
ma-136	260	32	=	=	SYM
ma-136	261	1	λ̄[p+1,q	λ̄[p+1,q	NOUN
ma-136	261	2	]	]	X
ma-136	261	3	(	(	PUNCT
ma-136	261	4	f	f	PROPN
ma-136	261	5	−	−	PROPN
ma-136	261	6	z	z	PROPN
ma-136	261	7	)	)	PUNCT
ma-136	261	8	=	=	SYM
ma-136	261	9	σ[p+1,q	σ[p+1,q	NOUN
ma-136	261	10	]	]	PUNCT
ma-136	261	11	(	(	PUNCT
ma-136	261	12	f	f	X
ma-136	261	13	)	)	PUNCT
ma-136	261	14	=	=	SYM
ma-136	261	15	µ	µ	X
ma-136	261	16	,	,	PUNCT
ma-136	261	17	(	(	PUNCT
ma-136	261	18	j	j	NOUN
ma-136	261	19	=	=	SYM
ma-136	261	20	1	1	NUM
ma-136	261	21	,	,	PUNCT
ma-136	261	22	2	2	NUM
ma-136	261	23	,	,	PUNCT
ma-136	261	24	...	...	PUNCT
ma-136	261	25	)	)	PUNCT
ma-136	261	26	.	.	PUNCT
ma-136	262	1	theorem	theorem	VERB
ma-136	262	2	1.10	1.10	NUM
ma-136	262	3	assume	assume	VERB
ma-136	262	4	that	that	SCONJ
ma-136	262	5	the	the	DET
ma-136	262	6	assumptions	assumption	NOUN
ma-136	262	7	of	of	ADP
ma-136	262	8	theorem	theorem	ADJ
ma-136	262	9	1.3	1.3	NUM
ma-136	262	10	or	or	CCONJ
ma-136	262	11	theorem	theorem	VERB
ma-136	262	12	1.4	1.4	NUM
ma-136	262	13	hold	hold	NOUN
ma-136	262	14	.	.	PUNCT
ma-136	263	1	then	then	ADV
ma-136	263	2	every	every	DET
ma-136	263	3	solution	solution	NOUN
ma-136	263	4	f	f	PROPN
ma-136	263	5	6≡	6≡	NUM
ma-136	263	6	0	0	NUM
ma-136	263	7	of	of	ADP
ma-136	263	8	equation	equation	NOUN
ma-136	263	9	(	(	PUNCT
ma-136	263	10	1.1	1.1	NUM
ma-136	263	11	)	)	PUNCT
ma-136	263	12	satisfies	satisfie	NOUN
ma-136	263	13	λ̄[p	λ̄[p	PROPN
ma-136	263	14	,	,	PUNCT
ma-136	263	15	q	q	X
ma-136	263	16	]	]	X
ma-136	263	17	(	(	PUNCT
ma-136	263	18	f	f	X
ma-136	263	19	(	(	PUNCT
ma-136	263	20	j	j	PROPN
ma-136	263	21	)	)	PUNCT
ma-136	263	22	−	−	PROPN
ma-136	263	23	z	z	NOUN
ma-136	263	24	)	)	PUNCT
ma-136	264	1	=	=	SYM
ma-136	264	2	λ[p	λ[p	NUM
ma-136	264	3	,	,	PUNCT
ma-136	264	4	q	q	X
ma-136	264	5	]	]	X
ma-136	264	6	(	(	PUNCT
ma-136	264	7	f	f	PROPN
ma-136	264	8	−	−	PROPN
ma-136	264	9	z	z	PROPN
ma-136	264	10	)	)	PUNCT
ma-136	264	11	=	=	SYM
ma-136	264	12	σ[p	σ[p	NOUN
ma-136	264	13	,	,	PUNCT
ma-136	264	14	q	q	X
ma-136	264	15	]	]	X
ma-136	264	16	(	(	PUNCT
ma-136	264	17	f	f	X
ma-136	264	18	)	)	PUNCT
ma-136	264	19	=	=	NOUN
ma-136	264	20	∞	∞	NOUN
ma-136	264	21	,	,	PUNCT
ma-136	264	22	λ̄[p+1,q	λ̄[p+1,q	NOUN
ma-136	264	23	]	]	X
ma-136	264	24	(	(	PUNCT
ma-136	264	25	f	f	X
ma-136	264	26	(	(	PUNCT
ma-136	264	27	j	j	PROPN
ma-136	264	28	)	)	PUNCT
ma-136	264	29	−	−	PROPN
ma-136	264	30	z	z	NOUN
ma-136	264	31	)	)	PUNCT
ma-136	264	32	=	=	SYM
ma-136	265	1	λ̄[p+1,q	λ̄[p+1,q	NOUN
ma-136	265	2	]	]	X
ma-136	265	3	(	(	PUNCT
ma-136	265	4	f	f	PROPN
ma-136	265	5	−	−	PROPN
ma-136	265	6	z	z	PROPN
ma-136	265	7	)	)	PUNCT
ma-136	265	8	=	=	SYM
ma-136	265	9	σ[p+1,q	σ[p+1,q	NOUN
ma-136	265	10	]	]	PUNCT
ma-136	265	11	(	(	PUNCT
ma-136	265	12	f	f	X
ma-136	265	13	)	)	PUNCT
ma-136	265	14	=	=	SYM
ma-136	265	15	µ	µ	X
ma-136	265	16	,	,	PUNCT
ma-136	265	17	(	(	PUNCT
ma-136	265	18	j	j	NOUN
ma-136	265	19	=	=	SYM
ma-136	265	20	1	1	NUM
ma-136	265	21	,	,	PUNCT
ma-136	265	22	2	2	NUM
ma-136	265	23	,	,	PUNCT
ma-136	265	24	...	...	PUNCT
ma-136	265	25	)	)	PUNCT
ma-136	265	26	.	.	PUNCT
ma-136	266	1	theorem	theorem	VERB
ma-136	266	2	1.11	1.11	NUM
ma-136	266	3	assume	assume	VERB
ma-136	266	4	that	that	SCONJ
ma-136	266	5	the	the	DET
ma-136	266	6	assumptions	assumption	NOUN
ma-136	266	7	of	of	ADP
ma-136	266	8	one	one	NUM
ma-136	266	9	of	of	ADP
ma-136	266	10	theorem	theorem	ADJ
ma-136	266	11	1.5	1.5	NUM
ma-136	266	12	to	to	PART
ma-136	266	13	theorem	theorem	VERB
ma-136	266	14	1.8	1.8	NUM
ma-136	266	15	hold	hold	NOUN
ma-136	266	16	.	.	PUNCT
ma-136	267	1	then	then	ADV
ma-136	267	2	every	every	DET
ma-136	267	3	meromorphic	meromorphic	ADJ
ma-136	267	4	(	(	PUNCT
ma-136	267	5	or	or	CCONJ
ma-136	267	6	analytic	analytic	ADJ
ma-136	267	7	)	)	PUNCT
ma-136	267	8	solution	solution	NOUN
ma-136	267	9	f	f	PROPN
ma-136	267	10	6≡	6≡	NUM
ma-136	267	11	0	0	NUM
ma-136	267	12	of	of	ADP
ma-136	267	13	equation	equation	NOUN
ma-136	267	14	(	(	PUNCT
ma-136	267	15	1.2	1.2	NUM
ma-136	267	16	)	)	PUNCT
ma-136	267	17	satisfies	satisfie	NOUN
ma-136	267	18	λ̄[p	λ̄[p	PROPN
ma-136	267	19	,	,	PUNCT
ma-136	267	20	q	q	X
ma-136	267	21	]	]	X
ma-136	267	22	(	(	PUNCT
ma-136	267	23	f	f	X
ma-136	267	24	(	(	PUNCT
ma-136	267	25	j	j	PROPN
ma-136	267	26	)	)	PUNCT
ma-136	267	27	−	−	PROPN
ma-136	267	28	z	z	NOUN
ma-136	267	29	)	)	PUNCT
ma-136	268	1	=	=	SYM
ma-136	268	2	λ[p	λ[p	NUM
ma-136	268	3	,	,	PUNCT
ma-136	268	4	q	q	X
ma-136	268	5	]	]	X
ma-136	268	6	(	(	PUNCT
ma-136	268	7	f	f	PROPN
ma-136	268	8	−	−	PROPN
ma-136	268	9	z	z	PROPN
ma-136	268	10	)	)	PUNCT
ma-136	268	11	=	=	SYM
ma-136	268	12	σ[p	σ[p	NOUN
ma-136	268	13	,	,	PUNCT
ma-136	268	14	q	q	X
ma-136	268	15	]	]	X
ma-136	268	16	(	(	PUNCT
ma-136	268	17	f	f	X
ma-136	268	18	)	)	PUNCT
ma-136	268	19	=	=	NOUN
ma-136	268	20	∞	∞	NOUN
ma-136	268	21	,	,	PUNCT
ma-136	268	22	λ̄[p+1,q	λ̄[p+1,q	NOUN
ma-136	268	23	]	]	X
ma-136	268	24	(	(	PUNCT
ma-136	268	25	f	f	X
ma-136	268	26	(	(	PUNCT
ma-136	268	27	j	j	PROPN
ma-136	268	28	)	)	PUNCT
ma-136	268	29	−	−	PROPN
ma-136	268	30	z	z	NOUN
ma-136	268	31	)	)	PUNCT
ma-136	268	32	=	=	SYM
ma-136	269	1	λ̄[p+1,q	λ̄[p+1,q	NOUN
ma-136	269	2	]	]	X
ma-136	269	3	(	(	PUNCT
ma-136	269	4	f	f	PROPN
ma-136	269	5	−	−	PROPN
ma-136	269	6	z	z	PROPN
ma-136	269	7	)	)	PUNCT
ma-136	269	8	=	=	SYM
ma-136	269	9	σ[p+1,q	σ[p+1,q	NOUN
ma-136	269	10	]	]	PUNCT
ma-136	269	11	(	(	PUNCT
ma-136	269	12	f	f	PROPN
ma-136	269	13	)	)	PUNCT
ma-136	269	14	≥	≥	PROPN
ma-136	269	15	µ	µ	NOUN
ma-136	269	16	,	,	PUNCT
ma-136	269	17	(	(	PUNCT
ma-136	269	18	j	j	NOUN
ma-136	269	19	=	=	SYM
ma-136	269	20	1	1	NUM
ma-136	269	21	,	,	PUNCT
ma-136	269	22	2	2	NUM
ma-136	269	23	,	,	PUNCT
ma-136	269	24	...	...	PUNCT
ma-136	269	25	)	)	PUNCT
ma-136	269	26	.	.	PUNCT
ma-136	270	1	2	2	X
ma-136	270	2	.	.	X
ma-136	270	3	some	some	DET
ma-136	270	4	lemmas	lemma	NOUN
ma-136	270	5	in	in	ADP
ma-136	270	6	this	this	DET
ma-136	270	7	section	section	NOUN
ma-136	270	8	we	we	PRON
ma-136	270	9	give	give	VERB
ma-136	270	10	some	some	DET
ma-136	270	11	lemmas	lemma	NOUN
ma-136	270	12	which	which	PRON
ma-136	270	13	are	be	AUX
ma-136	270	14	used	use	VERB
ma-136	270	15	in	in	ADP
ma-136	270	16	the	the	DET
ma-136	270	17	proofs	proof	NOUN
ma-136	270	18	of	of	ADP
ma-136	270	19	our	our	PRON
ma-136	270	20	theorems	theorem	NOUN
ma-136	270	21	.	.	PUNCT
ma-136	271	1	https://doi.org/10.28924/ada/ma.3.10	https://doi.org/10.28924/ada/ma.3.10	PROPN
ma-136	271	2	eur	eur	PROPN
ma-136	271	3	.	.	PUNCT
ma-136	272	1	j.	j.	PROPN
ma-136	272	2	math	math	PROPN
ma-136	272	3	.	.	PUNCT
ma-136	273	1	anal	anal	PROPN
ma-136	273	2	.	.	PUNCT
ma-136	274	1	10.28924	10.28924	NUM
ma-136	274	2	/	/	SYM
ma-136	274	3	ada	ada	NOUN
ma-136	274	4	/	/	SYM
ma-136	274	5	ma.3.10	ma.3.10	ADJ
ma-136	274	6	11	11	NUM
ma-136	274	7	lemma	lemma	PROPN
ma-136	274	8	2.1	2.1	NUM
ma-136	274	9	(	(	PUNCT
ma-136	274	10	[	[	X
ma-136	274	11	11	11	NUM
ma-136	274	12	]	]	PUNCT
ma-136	274	13	,	,	PUNCT
ma-136	274	14	theorem	theorem	VERB
ma-136	274	15	3.1	3.1	NUM
ma-136	274	16	)	)	PUNCT
ma-136	274	17	let	let	VERB
ma-136	274	18	k	k	PROPN
ma-136	274	19	and	and	CCONJ
ma-136	274	20	j	j	PROPN
ma-136	274	21	be	be	VERB
ma-136	274	22	integers	integer	NOUN
ma-136	274	23	satisfying	satisfy	VERB
ma-136	274	24	k	k	PROPN
ma-136	274	25	>	>	X
ma-136	274	26	j	j	PROPN
ma-136	274	27	≥	≥	PROPN
ma-136	274	28	0	0	NUM
ma-136	274	29	,	,	PUNCT
ma-136	274	30	and	and	CCONJ
ma-136	274	31	let	let	VERB
ma-136	274	32	ε	ε	PROPN
ma-136	274	33	>	>	X
ma-136	274	34	0	0	PUNCT
ma-136	275	1	and	and	CCONJ
ma-136	275	2	d	d	PROPN
ma-136	275	3	∈	∈	PROPN
ma-136	275	4	(	(	PUNCT
ma-136	275	5	0	0	NUM
ma-136	275	6	,	,	PUNCT
ma-136	275	7	1	1	NUM
ma-136	275	8	)	)	PUNCT
ma-136	275	9	.	.	PUNCT
ma-136	276	1	if	if	SCONJ
ma-136	276	2	f	f	PROPN
ma-136	276	3	is	be	AUX
ma-136	276	4	a	a	DET
ma-136	276	5	meromorphic	meromorphic	ADJ
ma-136	276	6	function	function	NOUN
ma-136	276	7	in	in	ADP
ma-136	276	8	d	d	PROPN
ma-136	276	9	such	such	ADJ
ma-136	276	10	that	that	SCONJ
ma-136	276	11	f	f	PROPN
ma-136	276	12	(	(	PUNCT
ma-136	276	13	j	j	NOUN
ma-136	276	14	)	)	PUNCT
ma-136	276	15	does	do	AUX
ma-136	276	16	not	not	PART
ma-136	276	17	vanish	vanish	VERB
ma-136	276	18	identically	identically	ADV
ma-136	276	19	,	,	PUNCT
ma-136	276	20	then	then	ADV
ma-136	276	21	for	for	ADP
ma-136	276	22	|z	|z	PROPN
ma-136	276	23	|	|	ADV
ma-136	276	24	/∈	/∈	PUNCT
ma-136	277	1	e1	e1	PROPN
ma-136	277	2	∣∣∣∣∣	∣∣∣∣∣	PROPN
ma-136	278	1	f	f	PROPN
ma-136	278	2	(	(	PUNCT
ma-136	278	3	k	k	NOUN
ma-136	278	4	)	)	PUNCT
ma-136	278	5	(	(	PUNCT
ma-136	278	6	z	z	X
ma-136	278	7	)	)	PUNCT
ma-136	278	8	f	f	PROPN
ma-136	278	9	(	(	PUNCT
ma-136	278	10	j	j	NOUN
ma-136	278	11	)	)	PUNCT
ma-136	278	12	(	(	PUNCT
ma-136	278	13	z	z	NOUN
ma-136	278	14	)	)	PUNCT
ma-136	279	1	∣∣∣∣∣	∣∣∣∣∣	ADP
ma-136	279	2	≤	≤	NOUN
ma-136	280	1	[	[	X
ma-136	280	2	(	(	PUNCT
ma-136	280	3	1	1	NUM
ma-136	280	4	1−	1−	NUM
ma-136	280	5	|z	|z	NOUN
ma-136	280	6	|	|	ADV
ma-136	280	7	)	)	PUNCT
ma-136	280	8	2+ε	2+ε	NUM
ma-136	280	9	max	max	PROPN
ma-136	280	10	{	{	PUNCT
ma-136	280	11	log	log	NOUN
ma-136	280	12	(	(	PUNCT
ma-136	280	13	1	1	NUM
ma-136	280	14	1−	1−	NUM
ma-136	280	15	|z	|z	NOUN
ma-136	280	16	|	|	ADV
ma-136	280	17	)	)	PUNCT
ma-136	280	18	;	;	PUNCT
ma-136	280	19	t	t	PROPN
ma-136	280	20	(	(	PUNCT
ma-136	280	21	s	s	X
ma-136	280	22	(	(	PUNCT
ma-136	280	23	|z	|z	PROPN
ma-136	280	24	|	|	NOUN
ma-136	280	25	)	)	PUNCT
ma-136	280	26	,	,	PUNCT
ma-136	280	27	f	f	PROPN
ma-136	280	28	)	)	PUNCT
ma-136	280	29	}	}	PUNCT
ma-136	280	30	]	]	PUNCT
ma-136	280	31	k−j	k−j	X
ma-136	280	32	,	,	PUNCT
ma-136	280	33	where	where	SCONJ
ma-136	280	34	e1	e1	VERB
ma-136	280	35	⊂	⊂	PROPN
ma-136	281	1	[	[	X
ma-136	281	2	0	0	NUM
ma-136	281	3	,	,	PUNCT
ma-136	281	4	1	1	NUM
ma-136	281	5	)	)	PUNCT
ma-136	281	6	is	be	AUX
ma-136	281	7	a	a	DET
ma-136	281	8	set	set	NOUN
ma-136	281	9	with	with	ADP
ma-136	281	10	∫	∫	PROPN
ma-136	281	11	e1	e1	PROPN
ma-136	281	12	dr	dr	PROPN
ma-136	281	13	1−r	1−r	PROPN
ma-136	281	14	<	<	X
ma-136	281	15	∞	∞	PROPN
ma-136	281	16	and	and	CCONJ
ma-136	281	17	s	s	PROPN
ma-136	281	18	(	(	PUNCT
ma-136	281	19	|z	|z	PROPN
ma-136	281	20	|	|	NOUN
ma-136	281	21	)	)	PUNCT
ma-136	281	22	=	=	PUNCT
ma-136	282	1	1−	1−	NUM
ma-136	282	2	d	d	NOUN
ma-136	282	3	(	(	PUNCT
ma-136	282	4	1−	1−	NUM
ma-136	282	5	|z	|z	PROPN
ma-136	282	6	|	|	NOUN
ma-136	282	7	)	)	PUNCT
ma-136	282	8	.	.	PUNCT
ma-136	283	1	lemma	lemma	PROPN
ma-136	283	2	2.2	2.2	NUM
ma-136	283	3	(	(	PUNCT
ma-136	283	4	[	[	X
ma-136	283	5	13	13	NUM
ma-136	283	6	]	]	PUNCT
ma-136	283	7	)	)	PUNCT
ma-136	283	8	let	let	VERB
ma-136	283	9	f	f	PRON
ma-136	283	10	be	be	AUX
ma-136	283	11	a	a	DET
ma-136	283	12	meromorphic	meromorphic	ADJ
ma-136	283	13	function	function	NOUN
ma-136	283	14	in	in	ADP
ma-136	283	15	the	the	DET
ma-136	283	16	unit	unit	NOUN
ma-136	283	17	disc	disc	VERB
ma-136	283	18	d	d	PROPN
ma-136	283	19	,	,	PUNCT
ma-136	283	20	and	and	CCONJ
ma-136	283	21	let	let	VERB
ma-136	283	22	k	k	PROPN
ma-136	283	23	≥	≥	NUM
ma-136	283	24	1	1	NUM
ma-136	283	25	be	be	AUX
ma-136	283	26	an	an	DET
ma-136	283	27	integer	integer	NOUN
ma-136	283	28	.	.	PUNCT
ma-136	284	1	then	then	ADV
ma-136	284	2	m	m	VERB
ma-136	284	3	(	(	PUNCT
ma-136	284	4	r	r	NOUN
ma-136	284	5	,	,	PUNCT
ma-136	284	6	f	f	PROPN
ma-136	284	7	(	(	PUNCT
ma-136	284	8	k	k	NOUN
ma-136	284	9	)	)	PUNCT
ma-136	284	10	f	f	NOUN
ma-136	284	11	)	)	PUNCT
ma-136	285	1	=	=	SYM
ma-136	285	2	s	s	X
ma-136	285	3	(	(	PUNCT
ma-136	285	4	r	r	NOUN
ma-136	285	5	,	,	PUNCT
ma-136	285	6	f	f	PROPN
ma-136	285	7	)	)	PUNCT
ma-136	285	8	,	,	PUNCT
ma-136	285	9	where	where	SCONJ
ma-136	285	10	s(r	s(r	PROPN
ma-136	285	11	,	,	PUNCT
ma-136	285	12	f	f	PROPN
ma-136	285	13	)	)	PUNCT
ma-136	285	14	=	=	PUNCT
ma-136	286	1	o	o	NOUN
ma-136	286	2	(	(	PUNCT
ma-136	286	3	log+	log+	PROPN
ma-136	286	4	t	t	X
ma-136	286	5	(	(	PUNCT
ma-136	286	6	r	r	NOUN
ma-136	286	7	,	,	PUNCT
ma-136	286	8	f	f	PROPN
ma-136	286	9	)	)	PUNCT
ma-136	287	1	+	+	CCONJ
ma-136	287	2	log	log	NOUN
ma-136	287	3	(	(	PUNCT
ma-136	287	4	1	1	NUM
ma-136	287	5	1−r	1−r	NUM
ma-136	287	6	)	)	PUNCT
ma-136	287	7	)	)	PUNCT
ma-136	287	8	,	,	PUNCT
ma-136	287	9	possibly	possibly	ADV
ma-136	287	10	outside	outside	ADP
ma-136	287	11	a	a	DET
ma-136	287	12	set	set	NOUN
ma-136	287	13	e2	e2	PROPN
ma-136	287	14	⊂	⊂	PROPN
ma-136	288	1	[	[	X
ma-136	288	2	0	0	NUM
ma-136	288	3	,	,	PUNCT
ma-136	288	4	1	1	NUM
ma-136	288	5	)	)	PUNCT
ma-136	288	6	with	with	ADP
ma-136	288	7	∫	∫	PROPN
ma-136	288	8	e2	e2	PROPN
ma-136	288	9	dr	dr	PROPN
ma-136	288	10	1−r	1−r	PROPN
ma-136	288	11	<	<	X
ma-136	288	12	∞.	∞.	PROPN
ma-136	288	13	lemma	lemma	PROPN
ma-136	288	14	2.3	2.3	NUM
ma-136	288	15	(	(	PUNCT
ma-136	288	16	[	[	X
ma-136	288	17	1	1	NUM
ma-136	288	18	]	]	PUNCT
ma-136	288	19	)	)	PUNCT
ma-136	288	20	let	let	VERB
ma-136	288	21	g	g	NOUN
ma-136	288	22	:	:	PUNCT
ma-136	288	23	(	(	PUNCT
ma-136	288	24	0	0	NUM
ma-136	288	25	,	,	PUNCT
ma-136	288	26	1	1	NUM
ma-136	288	27	)	)	PUNCT
ma-136	288	28	→	→	SYM
ma-136	288	29	r	r	NOUN
ma-136	288	30	and	and	CCONJ
ma-136	288	31	h	h	NOUN
ma-136	288	32	:	:	PUNCT
ma-136	288	33	(	(	PUNCT
ma-136	288	34	0	0	NUM
ma-136	288	35	,	,	PUNCT
ma-136	288	36	1	1	NUM
ma-136	288	37	)	)	PUNCT
ma-136	288	38	→	→	SYM
ma-136	288	39	r	r	NOUN
ma-136	288	40	be	be	VERB
ma-136	288	41	monotone	monotone	ADJ
ma-136	288	42	increasing	increase	VERB
ma-136	288	43	functions	function	NOUN
ma-136	288	44	such	such	ADJ
ma-136	288	45	that	that	PRON
ma-136	288	46	g	g	NOUN
ma-136	288	47	(	(	PUNCT
ma-136	288	48	r	r	NOUN
ma-136	288	49	)	)	PUNCT
ma-136	288	50	≤	≤	NUM
ma-136	288	51	h	h	NOUN
ma-136	288	52	(	(	PUNCT
ma-136	288	53	r	r	NOUN
ma-136	288	54	)	)	PUNCT
ma-136	288	55	holds	hold	VERB
ma-136	288	56	outside	outside	ADP
ma-136	288	57	of	of	ADP
ma-136	288	58	an	an	DET
ma-136	288	59	exceptional	exceptional	ADJ
ma-136	288	60	set	set	NOUN
ma-136	289	1	e3	e3	NOUN
ma-136	289	2	⊂	⊂	PRON
ma-136	290	1	[	[	X
ma-136	290	2	0	0	NUM
ma-136	290	3	,	,	PUNCT
ma-136	290	4	1	1	NUM
ma-136	290	5	)	)	PUNCT
ma-136	290	6	for	for	ADP
ma-136	290	7	which	which	PRON
ma-136	290	8	∫	∫	PROPN
ma-136	290	9	e3	e3	PROPN
ma-136	290	10	dr	dr	PROPN
ma-136	290	11	1−r	1−r	PROPN
ma-136	290	12	<	<	X
ma-136	290	13	∞.	∞.	PROPN
ma-136	290	14	then	then	ADV
ma-136	290	15	there	there	PRON
ma-136	290	16	exists	exist	VERB
ma-136	290	17	a	a	DET
ma-136	290	18	constant	constant	ADJ
ma-136	290	19	d	d	X
ma-136	290	20	∈	∈	PROPN
ma-136	290	21	(	(	PUNCT
ma-136	290	22	0	0	NUM
ma-136	290	23	,	,	PUNCT
ma-136	290	24	1	1	NUM
ma-136	290	25	)	)	PUNCT
ma-136	290	26	such	such	ADJ
ma-136	290	27	that	that	SCONJ
ma-136	290	28	if	if	SCONJ
ma-136	290	29	s	s	X
ma-136	290	30	(	(	PUNCT
ma-136	290	31	r	r	NOUN
ma-136	290	32	)	)	PUNCT
ma-136	290	33	=	=	SYM
ma-136	291	1	1−	1−	NUM
ma-136	291	2	d	d	NOUN
ma-136	291	3	(	(	PUNCT
ma-136	291	4	1−	1−	NUM
ma-136	291	5	r	r	NOUN
ma-136	291	6	)	)	PUNCT
ma-136	291	7	,	,	PUNCT
ma-136	291	8	then	then	ADV
ma-136	291	9	g	g	PROPN
ma-136	291	10	(	(	PUNCT
ma-136	291	11	r	r	NOUN
ma-136	291	12	)	)	PUNCT
ma-136	291	13	≤	≤	NUM
ma-136	291	14	h	h	NOUN
ma-136	291	15	(	(	PUNCT
ma-136	291	16	s	s	X
ma-136	291	17	(	(	PUNCT
ma-136	291	18	r	r	NOUN
ma-136	291	19	)	)	PUNCT
ma-136	291	20	)	)	PUNCT
ma-136	291	21	for	for	ADP
ma-136	291	22	all	all	DET
ma-136	291	23	r	r	NOUN
ma-136	291	24	∈	∈	PROPN
ma-136	292	1	[	[	X
ma-136	292	2	0	0	NUM
ma-136	292	3	,	,	PUNCT
ma-136	292	4	1	1	NUM
ma-136	292	5	)	)	PUNCT
ma-136	292	6	.	.	PUNCT
ma-136	293	1	lemma	lemma	PROPN
ma-136	293	2	2.4	2.4	NUM
ma-136	293	3	(	(	PUNCT
ma-136	293	4	[	[	X
ma-136	293	5	3	3	NUM
ma-136	293	6	]	]	PUNCT
ma-136	293	7	)	)	PUNCT
ma-136	293	8	let	let	VERB
ma-136	293	9	p	p	PRON
ma-136	293	10	≥	≥	PRON
ma-136	293	11	q	q	NOUN
ma-136	293	12	≥	≥	NUM
ma-136	293	13	1	1	NUM
ma-136	293	14	be	be	VERB
ma-136	293	15	integers	integer	NOUN
ma-136	293	16	.	.	PUNCT
ma-136	294	1	if	if	SCONJ
ma-136	294	2	a0	a0	PROPN
ma-136	294	3	(	(	PUNCT
ma-136	294	4	z	z	NOUN
ma-136	294	5	)	)	PUNCT
ma-136	294	6	,	,	PUNCT
ma-136	294	7	...	...	PUNCT
ma-136	294	8	,	,	PUNCT
ma-136	294	9	ak−1	ak−1	INTJ
ma-136	294	10	(	(	PUNCT
ma-136	294	11	z	z	NOUN
ma-136	294	12	)	)	PUNCT
ma-136	294	13	are	be	AUX
ma-136	294	14	analytic	analytic	ADJ
ma-136	294	15	functions	function	NOUN
ma-136	294	16	of	of	ADP
ma-136	294	17	[	[	X
ma-136	294	18	p	p	X
ma-136	294	19	,	,	PUNCT
ma-136	294	20	q]−order	q]−order	NOUN
ma-136	294	21	in	in	ADP
ma-136	294	22	the	the	DET
ma-136	294	23	unit	unit	NOUN
ma-136	294	24	disc	disc	NOUN
ma-136	294	25	d	d	PROPN
ma-136	294	26	,	,	PUNCT
ma-136	294	27	then	then	ADV
ma-136	294	28	every	every	DET
ma-136	294	29	solution	solution	NOUN
ma-136	294	30	f	f	PROPN
ma-136	294	31	6≡	6≡	NUM
ma-136	294	32	0	0	NUM
ma-136	294	33	of	of	ADP
ma-136	294	34	(	(	PUNCT
ma-136	294	35	1.1	1.1	NUM
ma-136	294	36	)	)	PUNCT
ma-136	294	37	satisfies	satisfy	VERB
ma-136	294	38	σ[p+1,q	σ[p+1,q	NOUN
ma-136	294	39	]	]	PUNCT
ma-136	294	40	(	(	PUNCT
ma-136	294	41	f	f	X
ma-136	294	42	)	)	PUNCT
ma-136	294	43	=	=	SYM
ma-136	295	1	σm,[p+1,q	σm,[p+1,q	X
ma-136	295	2	]	]	PUNCT
ma-136	295	3	(	(	PUNCT
ma-136	295	4	f	f	PROPN
ma-136	295	5	)	)	PUNCT
ma-136	295	6	≤	≤	PROPN
ma-136	295	7	max	max	PROPN
ma-136	295	8	{	{	PUNCT
ma-136	295	9	σm,[p	σm,[p	PROPN
ma-136	295	10	,	,	PUNCT
ma-136	295	11	q	q	X
ma-136	295	12	]	]	X
ma-136	295	13	(	(	PUNCT
ma-136	295	14	aj	aj	PROPN
ma-136	295	15	)	)	PUNCT
ma-136	295	16	:	:	PUNCT
ma-136	296	1	j	j	X
ma-136	296	2	=	=	SYM
ma-136	296	3	0	0	PROPN
ma-136	296	4	,	,	PUNCT
ma-136	296	5	1	1	NUM
ma-136	296	6	,	,	PUNCT
ma-136	296	7	...	...	PUNCT
ma-136	296	8	,	,	PUNCT
ma-136	296	9	k	k	PROPN
ma-136	296	10	−	−	PROPN
ma-136	296	11	1	1	NUM
ma-136	296	12	}	}	PUNCT
ma-136	296	13	.	.	PUNCT
ma-136	297	1	lemma	lemma	PROPN
ma-136	297	2	2.5	2.5	NUM
ma-136	297	3	(	(	PUNCT
ma-136	297	4	[	[	X
ma-136	297	5	4	4	NUM
ma-136	297	6	,	,	PUNCT
ma-136	297	7	18	18	NUM
ma-136	297	8	]	]	PUNCT
ma-136	297	9	)	)	PUNCT
ma-136	297	10	let	let	VERB
ma-136	297	11	p	p	PRON
ma-136	297	12	≥	≥	PRON
ma-136	297	13	q	q	NOUN
ma-136	297	14	≥	≥	NUM
ma-136	297	15	1	1	NUM
ma-136	297	16	be	be	VERB
ma-136	297	17	integers	integer	NOUN
ma-136	297	18	.	.	PUNCT
ma-136	298	1	if	if	SCONJ
ma-136	298	2	f	f	PROPN
ma-136	298	3	and	and	CCONJ
ma-136	298	4	g	g	PROPN
ma-136	298	5	are	be	AUX
ma-136	298	6	non	non	ADJ
ma-136	298	7	-	-	ADJ
ma-136	298	8	constant	constant	ADJ
ma-136	298	9	meromorphic	meromorphic	ADJ
ma-136	298	10	functions	function	NOUN
ma-136	298	11	of	of	ADP
ma-136	298	12	[	[	X
ma-136	298	13	p	p	X
ma-136	298	14	,	,	PUNCT
ma-136	298	15	q]−order	q]−order	NOUN
ma-136	298	16	in	in	ADP
ma-136	298	17	d	d	PROPN
ma-136	298	18	,	,	PUNCT
ma-136	298	19	then	then	ADV
ma-136	298	20	we	we	PRON
ma-136	298	21	have	have	VERB
ma-136	298	22	(	(	PUNCT
ma-136	298	23	i	i	NOUN
ma-136	298	24	)	)	PUNCT
ma-136	298	25	σ[p	σ[p	PROPN
ma-136	298	26	,	,	PUNCT
ma-136	298	27	q	q	X
ma-136	298	28	]	]	X
ma-136	298	29	(	(	PUNCT
ma-136	298	30	f	f	X
ma-136	298	31	)	)	PUNCT
ma-136	298	32	=	=	SYM
ma-136	299	1	σ[p	σ[p	NOUN
ma-136	299	2	,	,	PUNCT
ma-136	299	3	q	q	X
ma-136	299	4	]	]	X
ma-136	299	5	(	(	PUNCT
ma-136	299	6	1	1	NUM
ma-136	299	7	f	f	NOUN
ma-136	299	8	)	)	PUNCT
ma-136	299	9	,	,	PUNCT
ma-136	299	10	σ[p	σ[p	PROPN
ma-136	299	11	,	,	PUNCT
ma-136	299	12	q	q	X
ma-136	299	13	]	]	X
ma-136	299	14	(	(	PUNCT
ma-136	299	15	af	af	X
ma-136	299	16	)	)	PUNCT
ma-136	299	17	=	=	SYM
ma-136	299	18	σ[p	σ[p	NOUN
ma-136	299	19	,	,	PUNCT
ma-136	299	20	q	q	X
ma-136	299	21	]	]	X
ma-136	299	22	(	(	PUNCT
ma-136	299	23	f	f	PROPN
ma-136	299	24	)	)	PUNCT
ma-136	299	25	and	and	CCONJ
ma-136	299	26	σ[p	σ[p	NOUN
ma-136	299	27	,	,	PUNCT
ma-136	299	28	q	q	X
ma-136	299	29	]	]	X
ma-136	299	30	(	(	PUNCT
ma-136	299	31	f	f	X
ma-136	299	32	+	+	CCONJ
ma-136	299	33	a	a	X
ma-136	299	34	)	)	PUNCT
ma-136	299	35	=	=	SYM
ma-136	299	36	σ[p	σ[p	NOUN
ma-136	299	37	,	,	PUNCT
ma-136	299	38	q	q	X
ma-136	299	39	]	]	X
ma-136	299	40	(	(	PUNCT
ma-136	299	41	f	f	PROPN
ma-136	299	42	)	)	PUNCT
ma-136	299	43	(	(	PUNCT
ma-136	299	44	a	a	DET
ma-136	299	45	∈	∈	PROPN
ma-136	299	46	c∗	c∗	NOUN
ma-136	299	47	)	)	PUNCT
ma-136	299	48	,	,	PUNCT
ma-136	299	49	(	(	PUNCT
ma-136	299	50	ii	ii	NOUN
ma-136	299	51	)	)	PUNCT
ma-136	299	52	σ[p	σ[p	NOUN
ma-136	299	53	,	,	PUNCT
ma-136	299	54	q	q	X
ma-136	299	55	]	]	X
ma-136	299	56	(	(	PUNCT
ma-136	299	57	f	f	NOUN
ma-136	299	58	′	′	NUM
ma-136	299	59	)	)	PUNCT
ma-136	299	60	=	=	SYM
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ma-136	300	5	(	(	PUNCT
ma-136	300	6	f	f	PROPN
ma-136	300	7	)	)	PUNCT
ma-136	300	8	,	,	PUNCT
ma-136	300	9	(	(	PUNCT
ma-136	300	10	iii	iii	X
ma-136	300	11	)	)	PUNCT
ma-136	300	12	σ[p	σ[p	NOUN
ma-136	300	13	,	,	PUNCT
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ma-136	300	15	]	]	X
ma-136	300	16	(	(	PUNCT
ma-136	300	17	f	f	X
ma-136	300	18	+	+	CCONJ
ma-136	300	19	g	g	NOUN
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ma-136	300	22	max	max	NOUN
ma-136	300	23	{	{	PUNCT
ma-136	300	24	σ[p	σ[p	PROPN
ma-136	300	25	,	,	PUNCT
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ma-136	300	27	]	]	X
ma-136	300	28	(	(	PUNCT
ma-136	300	29	f	f	PROPN
ma-136	300	30	)	)	PUNCT
ma-136	300	31	,	,	PUNCT
ma-136	300	32	σ[p	σ[p	PROPN
ma-136	300	33	,	,	PUNCT
ma-136	300	34	q	q	X
ma-136	300	35	]	]	X
ma-136	300	36	(	(	PUNCT
ma-136	300	37	g	g	NOUN
ma-136	300	38	)	)	PUNCT
ma-136	300	39	}	}	PUNCT
ma-136	300	40	,	,	PUNCT
ma-136	300	41	(	(	PUNCT
ma-136	300	42	iv	iv	X
ma-136	300	43	)	)	PUNCT
ma-136	300	44	σ[p	σ[p	NOUN
ma-136	300	45	,	,	PUNCT
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ma-136	300	47	]	]	X
ma-136	300	48	(	(	PUNCT
ma-136	300	49	f	f	NOUN
ma-136	300	50	g	g	NOUN
ma-136	300	51	)	)	PUNCT
ma-136	300	52	≤	≤	NUM
ma-136	300	53	max	max	NOUN
ma-136	300	54	{	{	PUNCT
ma-136	300	55	σ[p	σ[p	PROPN
ma-136	300	56	,	,	PUNCT
ma-136	300	57	q	q	X
ma-136	300	58	]	]	X
ma-136	300	59	(	(	PUNCT
ma-136	300	60	f	f	PROPN
ma-136	300	61	)	)	PUNCT
ma-136	300	62	,	,	PUNCT
ma-136	300	63	σ[p	σ[p	PROPN
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ma-136	300	66	]	]	X
ma-136	300	67	(	(	PUNCT
ma-136	300	68	g	g	NOUN
ma-136	300	69	)	)	PUNCT
ma-136	300	70	}	}	PUNCT
ma-136	300	71	,	,	PUNCT
ma-136	300	72	if	if	SCONJ
ma-136	300	73	σ[p	σ[p	NOUN
ma-136	300	74	,	,	PUNCT
ma-136	300	75	q	q	X
ma-136	300	76	]	]	X
ma-136	300	77	(	(	PUNCT
ma-136	300	78	f	f	PROPN
ma-136	300	79	)	)	PUNCT
ma-136	300	80	>	>	X
ma-136	301	1	σ[p	σ[p	PROPN
ma-136	301	2	,	,	PUNCT
ma-136	301	3	q	q	X
ma-136	301	4	]	]	X
ma-136	301	5	(	(	PUNCT
ma-136	301	6	g	g	NOUN
ma-136	301	7	)	)	PUNCT
ma-136	301	8	,	,	PUNCT
ma-136	301	9	then	then	ADV
ma-136	301	10	we	we	PRON
ma-136	301	11	obtain	obtain	VERB
ma-136	301	12	σ[p	σ[p	NOUN
ma-136	301	13	,	,	PUNCT
ma-136	301	14	q	q	X
ma-136	301	15	]	]	X
ma-136	301	16	(	(	PUNCT
ma-136	301	17	f	f	X
ma-136	301	18	+	+	CCONJ
ma-136	301	19	g	g	NOUN
ma-136	301	20	)	)	PUNCT
ma-136	301	21	=	=	SYM
ma-136	302	1	σ[p	σ[p	NOUN
ma-136	302	2	,	,	PUNCT
ma-136	302	3	q	q	X
ma-136	302	4	]	]	X
ma-136	302	5	(	(	PUNCT
ma-136	302	6	f	f	NOUN
ma-136	302	7	g	g	NOUN
ma-136	302	8	)	)	PUNCT
ma-136	302	9	=	=	SYM
ma-136	303	1	σ[p	σ[p	NOUN
ma-136	303	2	,	,	PUNCT
ma-136	303	3	q	q	X
ma-136	303	4	]	]	X
ma-136	303	5	(	(	PUNCT
ma-136	303	6	f	f	PROPN
ma-136	303	7	)	)	PUNCT
ma-136	303	8	.	.	PUNCT
ma-136	304	1	lemma	lemma	PROPN
ma-136	304	2	2.6	2.6	NUM
ma-136	304	3	(	(	PUNCT
ma-136	304	4	[	[	X
ma-136	304	5	4	4	NUM
ma-136	304	6	]	]	PUNCT
ma-136	304	7	)	)	PUNCT
ma-136	304	8	let	let	VERB
ma-136	304	9	p	p	PRON
ma-136	304	10	≥	≥	PRON
ma-136	304	11	q	q	NOUN
ma-136	304	12	≥	≥	NUM
ma-136	304	13	1	1	NUM
ma-136	304	14	be	be	AUX
ma-136	304	15	integers	integer	NOUN
ma-136	304	16	.	.	PUNCT
ma-136	305	1	let	let	VERB
ma-136	305	2	a0	a0	PROPN
ma-136	305	3	,	,	PUNCT
ma-136	305	4	...	...	PUNCT
ma-136	305	5	,	,	PUNCT
ma-136	305	6	ak−1	ak−1	PROPN
ma-136	305	7	and	and	CCONJ
ma-136	305	8	f	f	PROPN
ma-136	305	9	6≡	6≡	PRON
ma-136	305	10	0	0	NUM
ma-136	305	11	be	be	AUX
ma-136	305	12	finite	finite	NOUN
ma-136	306	1	[	[	X
ma-136	306	2	p	p	X
ma-136	306	3	,	,	PUNCT
ma-136	306	4	q]−order	q]−order	ADJ
ma-136	306	5	analytic	analytic	ADJ
ma-136	306	6	functions	function	NOUN
ma-136	306	7	in	in	ADP
ma-136	306	8	the	the	DET
ma-136	306	9	unit	unit	NOUN
ma-136	306	10	disc	disc	VERB
ma-136	306	11	d.	d.	PROPN
ma-136	306	12	if	if	SCONJ
ma-136	306	13	f	f	PROPN
ma-136	306	14	is	be	AUX
ma-136	306	15	a	a	DET
ma-136	306	16	solution	solution	NOUN
ma-136	306	17	with	with	ADP
ma-136	306	18	σ[p	σ[p	NOUN
ma-136	306	19	,	,	PUNCT
ma-136	306	20	q	q	X
ma-136	306	21	]	]	X
ma-136	306	22	(	(	PUNCT
ma-136	306	23	f	f	X
ma-136	306	24	)	)	PUNCT
ma-136	307	1	=	=	NOUN
ma-136	307	2	∞	∞	NOUN
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ma-136	307	4	σ[p+1,q	σ[p+1,q	NOUN
ma-136	307	5	]	]	PUNCT
ma-136	307	6	(	(	PUNCT
ma-136	307	7	f	f	X
ma-136	307	8	)	)	PUNCT
ma-136	308	1	=	=	PUNCT
ma-136	308	2	σ	σ	NOUN
ma-136	308	3	<	<	X
ma-136	308	4	∞	∞	NOUN
ma-136	308	5	of	of	ADP
ma-136	308	6	equation	equation	NOUN
ma-136	308	7	f	f	X
ma-136	308	8	(	(	PUNCT
ma-136	308	9	k	k	NOUN
ma-136	308	10	)	)	PUNCT
ma-136	309	1	+	+	CCONJ
ma-136	309	2	ak−1	ak−1	ADV
ma-136	309	3	(	(	PUNCT
ma-136	309	4	z	z	NOUN
ma-136	309	5	)	)	PUNCT
ma-136	309	6	f	f	PROPN
ma-136	309	7	(	(	PUNCT
ma-136	309	8	k−1	k−1	PROPN
ma-136	309	9	)	)	PUNCT
ma-136	310	1	+	+	PUNCT
ma-136	310	2	·	·	PUNCT
ma-136	310	3	·	·	PUNCT
ma-136	310	4	·	·	PUNCT
ma-136	310	5	+	+	NUM
ma-136	310	6	a1	a1	NOUN
ma-136	310	7	(	(	PUNCT
ma-136	310	8	z	z	NOUN
ma-136	310	9	)	)	PUNCT
ma-136	310	10	f	f	NOUN
ma-136	310	11	′	′	NUM
ma-136	311	1	+	+	CCONJ
ma-136	311	2	a0	a0	PROPN
ma-136	311	3	(	(	PUNCT
ma-136	311	4	z	z	NOUN
ma-136	311	5	)	)	PUNCT
ma-136	311	6	f	f	NOUN
ma-136	311	7	=	=	SYM
ma-136	311	8	f	f	PROPN
ma-136	311	9	,	,	PUNCT
ma-136	311	10	(	(	PUNCT
ma-136	311	11	2.1	2.1	NUM
ma-136	311	12	)	)	PUNCT
ma-136	311	13	then	then	ADV
ma-136	311	14	λ̄[p	λ̄[p	NOUN
ma-136	311	15	,	,	PUNCT
ma-136	311	16	q	q	X
ma-136	311	17	]	]	X
ma-136	311	18	(	(	PUNCT
ma-136	311	19	f	f	X
ma-136	311	20	)	)	PUNCT
ma-136	312	1	=	=	SYM
ma-136	312	2	λ[p	λ[p	NUM
ma-136	312	3	,	,	PUNCT
ma-136	312	4	q	q	X
ma-136	312	5	]	]	X
ma-136	312	6	(	(	PUNCT
ma-136	312	7	f	f	X
ma-136	312	8	)	)	PUNCT
ma-136	312	9	=	=	SYM
ma-136	313	1	σ[p	σ[p	NOUN
ma-136	313	2	,	,	PUNCT
ma-136	313	3	q	q	X
ma-136	313	4	]	]	X
ma-136	313	5	(	(	PUNCT
ma-136	313	6	f	f	X
ma-136	313	7	)	)	PUNCT
ma-136	313	8	=	=	NOUN
ma-136	313	9	∞	∞	NOUN
ma-136	313	10	,	,	PUNCT
ma-136	313	11	λ̄[p+1,q	λ̄[p+1,q	NOUN
ma-136	313	12	]	]	X
ma-136	313	13	(	(	PUNCT
ma-136	313	14	f	f	X
ma-136	313	15	)	)	PUNCT
ma-136	313	16	=	=	SYM
ma-136	313	17	λ[p+1,q	λ[p+1,q	PROPN
ma-136	313	18	]	]	X
ma-136	313	19	(	(	PUNCT
ma-136	313	20	f	f	X
ma-136	313	21	)	)	PUNCT
ma-136	313	22	=	=	SYM
ma-136	313	23	σ[p+1,q	σ[p+1,q	NOUN
ma-136	313	24	]	]	PUNCT
ma-136	313	25	(	(	PUNCT
ma-136	313	26	f	f	X
ma-136	313	27	)	)	PUNCT
ma-136	313	28	=	=	SYM
ma-136	314	1	σ	σ	X
ma-136	314	2	.	.	PUNCT
ma-136	315	1	https://doi.org/10.28924/ada/ma.3.10	https://doi.org/10.28924/ada/ma.3.10	PROPN
ma-136	315	2	eur	eur	PROPN
ma-136	315	3	.	.	PUNCT
ma-136	316	1	j.	j.	PROPN
ma-136	316	2	math	math	PROPN
ma-136	316	3	.	.	PUNCT
ma-136	317	1	anal	anal	PROPN
ma-136	317	2	.	.	PUNCT
ma-136	318	1	10.28924	10.28924	NUM
ma-136	318	2	/	/	SYM
ma-136	318	3	ada	ada	NOUN
ma-136	318	4	/	/	SYM
ma-136	318	5	ma.3.10	ma.3.10	NOUN
ma-136	318	6	12by	12by	NOUN
ma-136	318	7	using	use	VERB
ma-136	318	8	the	the	DET
ma-136	318	9	same	same	ADJ
ma-136	318	10	arguments	argument	NOUN
ma-136	318	11	of	of	ADP
ma-136	318	12	the	the	DET
ma-136	318	13	proof	proof	NOUN
ma-136	318	14	of	of	ADP
ma-136	318	15	lemma	lemma	PROPN
ma-136	318	16	3.5	3.5	NUM
ma-136	318	17	in	in	ADP
ma-136	318	18	the	the	DET
ma-136	318	19	paper	paper	NOUN
ma-136	319	1	[	[	X
ma-136	319	2	14	14	NUM
ma-136	319	3	,	,	PUNCT
ma-136	319	4	p.	p.	NOUN
ma-136	319	5	4	4	NUM
ma-136	319	6	]	]	PUNCT
ma-136	319	7	,	,	PUNCT
ma-136	319	8	we	we	PRON
ma-136	319	9	obtain	obtain	AUX
ma-136	319	10	thefollowing	thefollowe	VERB
ma-136	319	11	lemma	lemma	PROPN
ma-136	319	12	in	in	ADP
ma-136	319	13	the	the	DET
ma-136	319	14	case	case	NOUN
ma-136	319	15	when	when	SCONJ
ma-136	319	16	σ[p	σ[p	NOUN
ma-136	319	17	,	,	PUNCT
ma-136	319	18	q	q	X
ma-136	319	19	]	]	X
ma-136	319	20	(	(	PUNCT
ma-136	319	21	f	f	X
ma-136	319	22	)	)	PUNCT
ma-136	320	1	=	=	PUNCT
ma-136	320	2	σ	σ	PROPN
ma-136	320	3	=	=	PROPN
ma-136	320	4	∞.	∞.	PROPN
ma-136	320	5	lemma	lemma	PROPN
ma-136	320	6	2.7	2.7	NUM
ma-136	320	7	let	let	VERB
ma-136	320	8	p	p	PRON
ma-136	320	9	≥	≥	PRON
ma-136	320	10	q	q	NOUN
ma-136	320	11	≥	≥	NUM
ma-136	320	12	1	1	NUM
ma-136	320	13	be	be	AUX
ma-136	320	14	integers	integer	NOUN
ma-136	320	15	.	.	PUNCT
ma-136	321	1	let	let	VERB
ma-136	321	2	aj	aj	PROPN
ma-136	321	3	(	(	PUNCT
ma-136	321	4	j	j	PROPN
ma-136	321	5	=	=	SYM
ma-136	321	6	0	0	PROPN
ma-136	321	7	,	,	PUNCT
ma-136	321	8	...	...	PUNCT
ma-136	321	9	,	,	PUNCT
ma-136	321	10	k	k	PROPN
ma-136	322	1	−	−	PROPN
ma-136	322	2	1	1	NUM
ma-136	322	3	)	)	PUNCT
ma-136	322	4	,	,	PUNCT
ma-136	322	5	f	f	PROPN
ma-136	322	6	6≡	6≡	NUM
ma-136	322	7	0	0	NUM
ma-136	322	8	be	be	AUX
ma-136	322	9	meromorphic	meromorphic	ADJ
ma-136	322	10	functions	function	NOUN
ma-136	322	11	in	in	ADP
ma-136	322	12	d	d	PROPN
ma-136	322	13	,	,	PUNCT
ma-136	322	14	and	and	CCONJ
ma-136	322	15	let	let	VERB
ma-136	322	16	f	f	PRON
ma-136	322	17	be	be	AUX
ma-136	322	18	a	a	DET
ma-136	322	19	solution	solution	NOUN
ma-136	322	20	of	of	ADP
ma-136	322	21	the	the	DET
ma-136	322	22	differential	differential	ADJ
ma-136	322	23	equation	equation	NOUN
ma-136	322	24	(	(	PUNCT
ma-136	322	25	2.1	2.1	NUM
ma-136	322	26	)	)	PUNCT
ma-136	322	27	satisfying	satisfy	VERB
ma-136	322	28	max	max	PROPN
ma-136	322	29	{	{	PUNCT
ma-136	322	30	σ[p	σ[p	PROPN
ma-136	322	31	,	,	PUNCT
ma-136	322	32	q	q	X
ma-136	322	33	]	]	X
ma-136	322	34	(	(	PUNCT
ma-136	322	35	aj	aj	PROPN
ma-136	322	36	)	)	PUNCT
ma-136	322	37	(	(	PUNCT
ma-136	322	38	j	j	NOUN
ma-136	322	39	=	=	SYM
ma-136	322	40	0	0	PROPN
ma-136	322	41	,	,	PUNCT
ma-136	322	42	...	...	PUNCT
ma-136	322	43	,	,	PUNCT
ma-136	323	1	k	k	PROPN
ma-136	323	2	−	−	PROPN
ma-136	323	3	1	1	NUM
ma-136	323	4	)	)	PUNCT
ma-136	323	5	,	,	PUNCT
ma-136	323	6	σ[p	σ[p	PROPN
ma-136	323	7	,	,	PUNCT
ma-136	323	8	q	q	X
ma-136	323	9	]	]	X
ma-136	323	10	(	(	PUNCT
ma-136	323	11	f	f	PROPN
ma-136	323	12	)	)	PUNCT
ma-136	323	13	}	}	PUNCT
ma-136	324	1	<	<	X
ma-136	324	2	σ[p	σ[p	NOUN
ma-136	324	3	,	,	PUNCT
ma-136	324	4	q	q	X
ma-136	324	5	]	]	X
ma-136	324	6	(	(	PUNCT
ma-136	324	7	f	f	X
ma-136	324	8	)	)	PUNCT
ma-136	325	1	=	=	PUNCT
ma-136	325	2	σ	σ	NOUN
ma-136	325	3	≤	≤	NOUN
ma-136	325	4	∞.	∞.	PROPN
ma-136	325	5	then	then	ADV
ma-136	325	6	we	we	PRON
ma-136	325	7	have	have	VERB
ma-136	325	8	λ[p	λ[p	NOUN
ma-136	325	9	,	,	PUNCT
ma-136	325	10	q	q	X
ma-136	325	11	]	]	X
ma-136	325	12	(	(	PUNCT
ma-136	325	13	f	f	X
ma-136	325	14	)	)	PUNCT
ma-136	325	15	=	=	SYM
ma-136	326	1	λ[p	λ[p	NUM
ma-136	326	2	,	,	PUNCT
ma-136	326	3	q	q	X
ma-136	326	4	]	]	X
ma-136	326	5	(	(	PUNCT
ma-136	326	6	f	f	X
ma-136	326	7	)	)	PUNCT
ma-136	326	8	=	=	SYM
ma-136	327	1	σ[p	σ[p	NOUN
ma-136	327	2	,	,	PUNCT
ma-136	327	3	q	q	X
ma-136	327	4	]	]	X
ma-136	327	5	(	(	PUNCT
ma-136	327	6	f	f	PROPN
ma-136	327	7	)	)	PUNCT
ma-136	327	8	and	and	CCONJ
ma-136	327	9	λ[p+1,q	λ[p+1,q	PROPN
ma-136	327	10	]	]	PUNCT
ma-136	327	11	(	(	PUNCT
ma-136	327	12	f	f	X
ma-136	327	13	)	)	PUNCT
ma-136	327	14	=	=	SYM
ma-136	327	15	λ[p+1,q	λ[p+1,q	PROPN
ma-136	327	16	]	]	X
ma-136	327	17	(	(	PUNCT
ma-136	327	18	f	f	X
ma-136	327	19	)	)	PUNCT
ma-136	327	20	=	=	SYM
ma-136	327	21	σ[p+1,q	σ[p+1,q	NOUN
ma-136	327	22	]	]	PUNCT
ma-136	327	23	(	(	PUNCT
ma-136	327	24	f	f	PROPN
ma-136	327	25	)	)	PUNCT
ma-136	327	26	.	.	PUNCT
ma-136	328	1	3	3	X
ma-136	328	2	.	.	X
ma-136	328	3	proofs	proof	NOUN
ma-136	328	4	of	of	ADP
ma-136	328	5	theorems	theorem	NOUN
ma-136	328	6	1.1	1.1	NUM
ma-136	328	7	to	to	PART
ma-136	328	8	1.8	1.8	NUM
ma-136	328	9	proof	proof	NOUN
ma-136	328	10	of	of	ADP
ma-136	328	11	theorem	theorem	ADJ
ma-136	328	12	1.1	1.1	NUM
ma-136	328	13	.	.	PUNCT
ma-136	328	14	suppose	suppose	VERB
ma-136	328	15	that	that	SCONJ
ma-136	328	16	every	every	DET
ma-136	328	17	solution	solution	NOUN
ma-136	328	18	f	f	PROPN
ma-136	328	19	of	of	ADP
ma-136	328	20	equation	equation	NOUN
ma-136	328	21	(	(	PUNCT
ma-136	328	22	1.1	1.1	NUM
ma-136	328	23	)	)	PUNCT
ma-136	328	24	not	not	PART
ma-136	328	25	being	be	AUX
ma-136	328	26	identically	identically	ADV
ma-136	328	27	equalto	equalto	NOUN
ma-136	328	28	0	0	NUM
ma-136	328	29	.	.	PUNCT
ma-136	328	30	from	from	ADP
ma-136	328	31	the	the	DET
ma-136	328	32	conditions	condition	NOUN
ma-136	328	33	of	of	ADP
ma-136	328	34	theorem	theorem	NOUN
ma-136	328	35	1.1	1.1	NUM
ma-136	328	36	,	,	PUNCT
ma-136	328	37	there	there	PRON
ma-136	328	38	exists	exist	VERB
ma-136	328	39	a	a	DET
ma-136	328	40	set	set	ADJ
ma-136	328	41	h	h	NOUN
ma-136	328	42	of	of	ADP
ma-136	328	43	complex	complex	ADJ
ma-136	328	44	numbers	number	NOUN
ma-136	328	45	satisfying	satisfy	VERB
ma-136	328	46	densdh1	densdh1	PROPN
ma-136	328	47	>	>	X
ma-136	328	48	0	0	PROPN
ma-136	328	49	,	,	PUNCT
ma-136	328	50	where	where	SCONJ
ma-136	328	51	h1	h1	VERB
ma-136	328	52	=	=	PRON
ma-136	328	53	{	{	PUNCT
ma-136	328	54	r	r	NOUN
ma-136	328	55	=	=	PUNCT
ma-136	328	56	|z	|z	PROPN
ma-136	329	1	|	|	ADV
ma-136	329	2	:	:	PUNCT
ma-136	329	3	z	z	PROPN
ma-136	329	4	∈	∈	PROPN
ma-136	329	5	h	h	NOUN
ma-136	330	1	⊆	⊆	NUM
ma-136	330	2	d	d	NOUN
ma-136	330	3	}	}	PUNCT
ma-136	330	4	.	.	PUNCT
ma-136	331	1	then	then	ADV
ma-136	331	2	h1	h1	PROPN
ma-136	331	3	is	be	AUX
ma-136	331	4	a	a	DET
ma-136	331	5	set	set	NOUN
ma-136	331	6	with	with	ADP
ma-136	331	7	∫h1	∫h1	PROPN
ma-136	331	8	dr	dr	PROPN
ma-136	331	9	1−r	1−r	PROPN
ma-136	331	10	=	=	PUNCT
ma-136	332	1	+	+	NOUN
ma-136	332	2	∞	∞	NOUN
ma-136	332	3	,	,	PUNCT
ma-136	332	4	suchthat	suchthat	VERB
ma-136	332	5	for	for	ADP
ma-136	332	6	z	z	PROPN
ma-136	332	7	∈	∈	PROPN
ma-136	332	8	h	h	NOUN
ma-136	332	9	we	we	PRON
ma-136	332	10	have	have	VERB
ma-136	332	11	(	(	PUNCT
ma-136	332	12	1.3	1.3	NUM
ma-136	332	13	)	)	PUNCT
ma-136	332	14	and	and	CCONJ
ma-136	332	15	(	(	PUNCT
ma-136	332	16	1.4	1.4	NUM
ma-136	332	17	)	)	PUNCT
ma-136	332	18	as	as	ADP
ma-136	332	19	|z	|z	PROPN
ma-136	332	20	|	|	PROPN
ma-136	332	21	→	→	SYM
ma-136	332	22	1−.	1−.	NUM
ma-136	332	23	by	by	ADP
ma-136	332	24	lemma	lemma	PROPN
ma-136	332	25	2.1	2.1	NUM
ma-136	332	26	,	,	PUNCT
ma-136	332	27	there	there	PRON
ma-136	332	28	exists	exist	VERB
ma-136	332	29	a	a	DET
ma-136	332	30	set	set	NOUN
ma-136	332	31	e1	e1	NOUN
ma-136	332	32	⊂	⊂	PUNCT
ma-136	333	1	[	[	X
ma-136	333	2	0	0	NUM
ma-136	333	3	,	,	PUNCT
ma-136	333	4	1)with	1)with	NUM
ma-136	333	5	∫e1	∫e1	PROPN
ma-136	333	6	dr	dr	PROPN
ma-136	333	7	1−r	1−r	PROPN
ma-136	333	8	<	<	X
ma-136	333	9	∞	∞	NUM
ma-136	333	10	such	such	ADJ
ma-136	333	11	that	that	PRON
ma-136	333	12	for	for	ADP
ma-136	333	13	|z	|z	PROPN
ma-136	333	14	|	|	PROPN
ma-136	333	15	/∈	/∈	PUNCT
ma-136	334	1	e1	e1	NOUN
ma-136	334	2	,	,	PUNCT
ma-136	334	3	we	we	PRON
ma-136	334	4	have	have	VERB
ma-136	334	5	for	for	ADP
ma-136	334	6	j	j	PROPN
ma-136	334	7	=	=	SYM
ma-136	334	8	1	1	NUM
ma-136	334	9	,	,	PUNCT
ma-136	334	10	...	...	PUNCT
ma-136	334	11	,	,	PUNCT
ma-136	334	12	k∣∣∣∣∣	k∣∣∣∣∣	PROPN
ma-136	334	13	f	f	X
ma-136	334	14	(	(	PUNCT
ma-136	334	15	j	j	PROPN
ma-136	334	16	)	)	PUNCT
ma-136	334	17	(	(	PUNCT
ma-136	334	18	z	z	X
ma-136	334	19	)	)	PUNCT
ma-136	334	20	f	f	NOUN
ma-136	334	21	(	(	PUNCT
ma-136	334	22	z	z	NOUN
ma-136	334	23	)	)	PUNCT
ma-136	334	24	∣∣∣∣∣	∣∣∣∣∣	ADP
ma-136	335	1	≤	≤	NOUN
ma-136	336	1	[	[	X
ma-136	336	2	(	(	PUNCT
ma-136	336	3	1	1	NUM
ma-136	336	4	1−	1−	NUM
ma-136	336	5	|z	|z	NOUN
ma-136	336	6	|	|	ADV
ma-136	336	7	)	)	PUNCT
ma-136	336	8	2+ε	2+ε	NUM
ma-136	336	9	max	max	PROPN
ma-136	336	10	{	{	PUNCT
ma-136	336	11	log	log	NOUN
ma-136	336	12	(	(	PUNCT
ma-136	336	13	1	1	NUM
ma-136	336	14	1−	1−	NUM
ma-136	336	15	|z	|z	NOUN
ma-136	336	16	|	|	ADV
ma-136	336	17	)	)	PUNCT
ma-136	336	18	,	,	PUNCT
ma-136	336	19	t	t	PROPN
ma-136	336	20	(	(	PUNCT
ma-136	336	21	s	s	X
ma-136	336	22	(	(	PUNCT
ma-136	336	23	|z	|z	PROPN
ma-136	336	24	|	|	NOUN
ma-136	336	25	)	)	PUNCT
ma-136	336	26	,	,	PUNCT
ma-136	336	27	f	f	PROPN
ma-136	336	28	)	)	PUNCT
ma-136	336	29	}	}	PUNCT
ma-136	337	1	]	]	X
ma-136	337	2	j	j	X
ma-136	337	3	,	,	PUNCT
ma-136	337	4	(	(	PUNCT
ma-136	337	5	3.1	3.1	NUM
ma-136	337	6	)	)	PUNCT
ma-136	337	7	where	where	SCONJ
ma-136	337	8	s	s	X
ma-136	337	9	(	(	PUNCT
ma-136	337	10	|z	|z	PROPN
ma-136	337	11	|	|	NOUN
ma-136	337	12	)	)	PUNCT
ma-136	337	13	=	=	PUNCT
ma-136	337	14	1−	1−	NUM
ma-136	337	15	d	d	NOUN
ma-136	337	16	(	(	PUNCT
ma-136	337	17	1−	1−	NUM
ma-136	337	18	|z	|z	PROPN
ma-136	337	19	|	|	NOUN
ma-136	337	20	)	)	PUNCT
ma-136	337	21	,	,	PUNCT
ma-136	337	22	d	d	PROPN
ma-136	337	23	∈	∈	PROPN
ma-136	337	24	(	(	PUNCT
ma-136	337	25	0	0	NUM
ma-136	337	26	,	,	PUNCT
ma-136	337	27	1	1	NUM
ma-136	337	28	)	)	PUNCT
ma-136	337	29	.	.	PUNCT
ma-136	338	1	from	from	ADP
ma-136	338	2	(	(	PUNCT
ma-136	338	3	1.1	1.1	NUM
ma-136	338	4	)	)	PUNCT
ma-136	338	5	,	,	PUNCT
ma-136	338	6	we	we	PRON
ma-136	338	7	get	get	VERB
ma-136	338	8	|a0	|a0	PROPN
ma-136	338	9	(	(	PUNCT
ma-136	338	10	z)|	z)|	ADP
ma-136	338	11	≤	≤	NOUN
ma-136	338	12	∣∣∣∣∣	∣∣∣∣∣	PROPN
ma-136	339	1	f	f	PROPN
ma-136	339	2	(	(	PUNCT
ma-136	339	3	k)f	k)f	PROPN
ma-136	339	4	∣∣∣∣∣+	∣∣∣∣∣+	PROPN
ma-136	339	5	|ak−1	|ak−1	NUM
ma-136	339	6	(	(	PUNCT
ma-136	339	7	z)|	z)|	X
ma-136	339	8	∣∣∣∣∣	∣∣∣∣∣	PROPN
ma-136	340	1	f	f	PROPN
ma-136	341	1	(	(	PUNCT
ma-136	341	2	k−1)f	k−1)f	PROPN
ma-136	341	3	∣∣∣∣∣+	∣∣∣∣∣+	PROPN
ma-136	341	4	·	·	PUNCT
ma-136	341	5	·	·	PUNCT
ma-136	341	6	·	·	PUNCT
ma-136	342	1	+	+	NUM
ma-136	342	2	|a1	|a1	NOUN
ma-136	342	3	(	(	PUNCT
ma-136	342	4	z)|	z)|	NOUN
ma-136	342	5	∣∣∣∣	∣∣∣∣	PROPN
ma-136	342	6	f	f	PROPN
ma-136	342	7	′f	′f	PROPN
ma-136	342	8	∣∣∣∣	∣∣∣∣	PROPN
ma-136	342	9	.	.	PUNCT
ma-136	343	1	(	(	PUNCT
ma-136	343	2	3.2	3.2	NUM
ma-136	343	3	)	)	PUNCT
ma-136	343	4	by	by	ADP
ma-136	343	5	(	(	PUNCT
ma-136	343	6	1.3	1.3	NUM
ma-136	343	7	)	)	PUNCT
ma-136	343	8	,	,	PUNCT
ma-136	343	9	we	we	PRON
ma-136	343	10	know	know	VERB
ma-136	343	11	that	that	SCONJ
ma-136	343	12	∃γ	∃γ	NOUN
ma-136	343	13	∈	∈	NOUN
ma-136	343	14	r	r	NOUN
ma-136	343	15	:	:	PUNCT
ma-136	343	16	lim	lim	PROPN
ma-136	343	17	inf	inf	PROPN
ma-136	343	18	|z	|z	PROPN
ma-136	343	19	|→1−,z∈h	|→1−,z∈h	PROPN
ma-136	343	20	logp	logp	NOUN
ma-136	344	1	|a0	|a0	PROPN
ma-136	344	2	(	(	PUNCT
ma-136	344	3	z)|	z)|	X
ma-136	344	4	(	(	PUNCT
ma-136	344	5	logq−1	logq−1	X
ma-136	344	6	(	(	PUNCT
ma-136	344	7	1	1	NUM
ma-136	344	8	1−|z	1−|z	NUM
ma-136	344	9	|	|	NOUN
ma-136	344	10	)	)	PUNCT
ma-136	344	11	)	)	PUNCT
ma-136	344	12	µ	µ	X
ma-136	344	13	>	>	X
ma-136	344	14	γ	γ	X
ma-136	344	15	>	>	X
ma-136	344	16	α	α	PROPN
ma-136	344	17	.	.	PUNCT
ma-136	345	1	obviously	obviously	ADV
ma-136	345	2	logp	logp	VERB
ma-136	345	3	|a0	|a0	PROPN
ma-136	346	1	(	(	PUNCT
ma-136	346	2	z)|	z)|	X
ma-136	346	3	(	(	PUNCT
ma-136	346	4	logq−1	logq−1	X
ma-136	346	5	(	(	PUNCT
ma-136	346	6	1	1	NUM
ma-136	346	7	1−|z	1−|z	NUM
ma-136	346	8	|	|	NOUN
ma-136	346	9	)	)	PUNCT
ma-136	346	10	)	)	PUNCT
ma-136	346	11	µ	µ	X
ma-136	346	12	>	>	X
ma-136	346	13	γ	γ	X
ma-136	346	14	>	>	X
ma-136	346	15	α	α	PROPN
ma-136	346	16	≥	≥	NOUN
ma-136	346	17	0	0	NUM
ma-136	346	18	(	(	PUNCT
ma-136	346	19	3.3	3.3	NUM
ma-136	346	20	)	)	PUNCT
ma-136	346	21	as	as	ADP
ma-136	346	22	|z	|z	PROPN
ma-136	346	23	|	|	PROPN
ma-136	346	24	→	→	SYM
ma-136	346	25	1−	1−	NUM
ma-136	346	26	for	for	ADP
ma-136	346	27	z	z	PROPN
ma-136	346	28	∈	∈	PROPN
ma-136	346	29	h.	h.	PROPN
ma-136	346	30	by	by	ADP
ma-136	346	31	(	(	PUNCT
ma-136	346	32	1.4	1.4	NUM
ma-136	346	33	)	)	PUNCT
ma-136	346	34	and	and	CCONJ
ma-136	346	35	(	(	PUNCT
ma-136	346	36	3.3	3.3	NUM
ma-136	346	37	)	)	PUNCT
ma-136	346	38	,	,	PUNCT
ma-136	346	39	we	we	PRON
ma-136	346	40	obtain	obtain	VERB
ma-136	346	41	|a0	|a0	PROPN
ma-136	346	42	(	(	PUNCT
ma-136	346	43	z)|	z)|	X
ma-136	346	44	>	>	X
ma-136	346	45	expp	expp	PROPN
ma-136	346	46	{	{	PUNCT
ma-136	346	47	γ	γ	X
ma-136	346	48	(	(	PUNCT
ma-136	346	49	logq−1	logq−1	X
ma-136	346	50	(	(	PUNCT
ma-136	346	51	1	1	NUM
ma-136	346	52	1−	1−	NUM
ma-136	346	53	|z	|z	NOUN
ma-136	346	54	|	|	ADV
ma-136	346	55	)	)	PUNCT
ma-136	346	56	)	)	PUNCT
ma-136	346	57	µ	µ	X
ma-136	346	58	}	}	PUNCT
ma-136	346	59	>	>	X
ma-136	346	60	expp	expp	PROPN
ma-136	346	61	{	{	PUNCT
ma-136	346	62	α	α	PROPN
ma-136	346	63	(	(	PUNCT
ma-136	346	64	logq−1	logq−1	X
ma-136	346	65	(	(	PUNCT
ma-136	346	66	1	1	NUM
ma-136	346	67	1−	1−	NUM
ma-136	346	68	|z	|z	NOUN
ma-136	346	69	|	|	ADV
ma-136	346	70	)	)	PUNCT
ma-136	346	71	)	)	PUNCT
ma-136	346	72	µ	µ	X
ma-136	346	73	}	}	PUNCT
ma-136	346	74	≥	≥	X
ma-136	346	75	|ai	|ai	NUM
ma-136	346	76	(	(	PUNCT
ma-136	346	77	z)|	z)|	INTJ
ma-136	346	78	(	(	PUNCT
ma-136	346	79	i	i	NOUN
ma-136	346	80	=	=	NOUN
ma-136	346	81	1	1	NUM
ma-136	346	82	,	,	PUNCT
ma-136	346	83	2	2	NUM
ma-136	346	84	,	,	PUNCT
ma-136	346	85	...	...	PUNCT
ma-136	346	86	,	,	PUNCT
ma-136	346	87	k	k	PROPN
ma-136	346	88	−	−	PROPN
ma-136	346	89	1	1	NUM
ma-136	346	90	)	)	PUNCT
ma-136	346	91	(	(	PUNCT
ma-136	346	92	3.4	3.4	NUM
ma-136	346	93	)	)	PUNCT
ma-136	346	94	https://doi.org/10.28924/ada/ma.3.10	https://doi.org/10.28924/ada/ma.3.10	ADV
ma-136	346	95	eur	eur	PROPN
ma-136	346	96	.	.	PUNCT
ma-136	347	1	j.	j.	PROPN
ma-136	347	2	math	math	PROPN
ma-136	347	3	.	.	PUNCT
ma-136	348	1	anal	anal	PROPN
ma-136	348	2	.	.	PUNCT
ma-136	349	1	10.28924	10.28924	NUM
ma-136	349	2	/	/	SYM
ma-136	349	3	ada	ada	NOUN
ma-136	349	4	/	/	SYM
ma-136	349	5	ma.3.10	ma.3.10	NOUN
ma-136	349	6	13as	13as	PROPN
ma-136	349	7	|z	|z	PROPN
ma-136	349	8	|	|	PROPN
ma-136	349	9	→	→	SYM
ma-136	349	10	1−	1−	NUM
ma-136	349	11	for	for	ADP
ma-136	349	12	z	z	PROPN
ma-136	349	13	∈	∈	PROPN
ma-136	349	14	h.	h.	NOUN
ma-136	349	15	applying	applying	NOUN
ma-136	349	16	(	(	PUNCT
ma-136	349	17	3.1	3.1	NUM
ma-136	349	18	)	)	PUNCT
ma-136	349	19	and	and	CCONJ
ma-136	349	20	(	(	PUNCT
ma-136	349	21	3.4	3.4	NUM
ma-136	349	22	)	)	PUNCT
ma-136	349	23	into	into	ADP
ma-136	349	24	(	(	PUNCT
ma-136	349	25	3.2	3.2	NUM
ma-136	349	26	)	)	PUNCT
ma-136	349	27	,	,	PUNCT
ma-136	349	28	we	we	PRON
ma-136	349	29	have	have	VERB
ma-136	349	30	expp	expp	ADJ
ma-136	349	31	{	{	PUNCT
ma-136	349	32	γ	γ	X
ma-136	349	33	(	(	PUNCT
ma-136	349	34	logq−1	logq−1	X
ma-136	349	35	(	(	PUNCT
ma-136	349	36	1	1	NUM
ma-136	349	37	1−	1−	NUM
ma-136	349	38	|z	|z	NOUN
ma-136	349	39	|	|	ADV
ma-136	349	40	)	)	PUNCT
ma-136	349	41	)	)	PUNCT
ma-136	349	42	µ	µ	X
ma-136	349	43	}	}	PUNCT
ma-136	349	44	≤	≤	NOUN
ma-136	349	45	|a0	|a0	PROPN
ma-136	350	1	(	(	PUNCT
ma-136	350	2	z)|	z)|	ADP
ma-136	350	3	≤	≤	PUNCT
ma-136	350	4	k	k	X
ma-136	351	1	[	[	X
ma-136	351	2	(	(	PUNCT
ma-136	351	3	1	1	NUM
ma-136	351	4	1−	1−	NUM
ma-136	351	5	|z	|z	NOUN
ma-136	351	6	|	|	ADV
ma-136	351	7	)	)	PUNCT
ma-136	351	8	2+ε	2+ε	NUM
ma-136	351	9	max	max	PROPN
ma-136	351	10	{	{	PUNCT
ma-136	351	11	log	log	NOUN
ma-136	351	12	(	(	PUNCT
ma-136	351	13	1	1	NUM
ma-136	351	14	1−	1−	NUM
ma-136	351	15	|z	|z	NOUN
ma-136	351	16	|	|	ADV
ma-136	351	17	)	)	PUNCT
ma-136	351	18	,	,	PUNCT
ma-136	351	19	t	t	PROPN
ma-136	351	20	(	(	PUNCT
ma-136	351	21	s	s	X
ma-136	351	22	(	(	PUNCT
ma-136	351	23	|z	|z	PROPN
ma-136	351	24	|	|	NOUN
ma-136	351	25	)	)	PUNCT
ma-136	351	26	,	,	PUNCT
ma-136	351	27	f	f	PROPN
ma-136	351	28	)	)	PUNCT
ma-136	351	29	}	}	PUNCT
ma-136	351	30	]	]	X
ma-136	351	31	k	k	X
ma-136	351	32	×	×	PROPN
ma-136	351	33	expp	expp	ADJ
ma-136	351	34	{	{	PUNCT
ma-136	351	35	α	α	PROPN
ma-136	351	36	(	(	PUNCT
ma-136	351	37	logq−1	logq−1	X
ma-136	351	38	(	(	PUNCT
ma-136	351	39	1	1	NUM
ma-136	351	40	1−	1−	NUM
ma-136	351	41	|z	|z	NOUN
ma-136	351	42	|	|	ADV
ma-136	351	43	)	)	PUNCT
ma-136	351	44	)	)	PUNCT
ma-136	351	45	µ	µ	X
ma-136	351	46	}	}	PUNCT
ma-136	351	47	holds	hold	VERB
ma-136	351	48	for	for	ADP
ma-136	351	49	all	all	PRON
ma-136	351	50	z	z	NOUN
ma-136	351	51	satisfying	satisfy	VERB
ma-136	351	52	|z	|z	PROPN
ma-136	351	53	|	|	PROPN
ma-136	351	54	∈	∈	PROPN
ma-136	351	55	h1\e1	h1\e1	PROPN
ma-136	351	56	as	as	ADP
ma-136	351	57	|z	|z	PROPN
ma-136	351	58	|	|	PROPN
ma-136	351	59	→	→	SYM
ma-136	351	60	1−.	1−.	NUM
ma-136	351	61	noting	note	VERB
ma-136	351	62	that	that	SCONJ
ma-136	351	63	γ	γ	PROPN
ma-136	351	64	>	>	X
ma-136	351	65	α	α	PROPN
ma-136	351	66	,	,	PUNCT
ma-136	351	67	by	by	ADP
ma-136	351	68	the	the	DET
ma-136	351	69	last	last	ADJ
ma-136	351	70	inequality	inequality	NOUN
ma-136	351	71	,	,	PUNCT
ma-136	351	72	weobtain	weobtain	NOUN
ma-136	351	73	exp	exp	NOUN
ma-136	351	74	(	(	PUNCT
ma-136	351	75	(	(	PUNCT
ma-136	351	76	1−	1−	NUM
ma-136	351	77	o	o	NOUN
ma-136	351	78	(	(	PUNCT
ma-136	351	79	1	1	NUM
ma-136	351	80	)	)	PUNCT
ma-136	351	81	)	)	PUNCT
ma-136	352	1	expp−1	expp−1	NOUN
ma-136	352	2	{	{	PUNCT
ma-136	352	3	γ	γ	X
ma-136	352	4	(	(	PUNCT
ma-136	352	5	logq−1	logq−1	X
ma-136	352	6	(	(	PUNCT
ma-136	352	7	1	1	NUM
ma-136	352	8	1−	1−	NUM
ma-136	352	9	|z	|z	NOUN
ma-136	352	10	|	|	ADV
ma-136	352	11	)	)	PUNCT
ma-136	352	12	)	)	PUNCT
ma-136	352	13	µ	µ	X
ma-136	352	14	}	}	PUNCT
ma-136	352	15	)	)	PUNCT
ma-136	352	16	≤	≤	PUNCT
ma-136	353	1	k	k	X
ma-136	353	2	(	(	PUNCT
ma-136	353	3	1	1	NUM
ma-136	353	4	1−	1−	NUM
ma-136	353	5	|z	|z	NOUN
ma-136	353	6	|	|	ADV
ma-136	353	7	)	)	PUNCT
ma-136	353	8	k(2+ε	k(2+ε	PROPN
ma-136	353	9	)	)	PUNCT
ma-136	354	1	t	t	PROPN
ma-136	354	2	k	k	X
ma-136	354	3	(	(	PUNCT
ma-136	354	4	s	s	X
ma-136	354	5	(	(	PUNCT
ma-136	354	6	|z	|z	PROPN
ma-136	354	7	|	|	NOUN
ma-136	354	8	)	)	PUNCT
ma-136	354	9	,	,	PUNCT
ma-136	354	10	f	f	PROPN
ma-136	354	11	)	)	PUNCT
ma-136	354	12	(	(	PUNCT
ma-136	354	13	3.5	3.5	NUM
ma-136	354	14	)	)	PUNCT
ma-136	354	15	for	for	ADP
ma-136	354	16	all	all	PRON
ma-136	354	17	z	z	NOUN
ma-136	354	18	satisfying	satisfy	VERB
ma-136	354	19	|z	|z	PROPN
ma-136	354	20	|	|	PROPN
ma-136	354	21	∈	∈	PROPN
ma-136	354	22	h1\e1	h1\e1	PROPN
ma-136	354	23	as	as	ADP
ma-136	354	24	|z	|z	PROPN
ma-136	354	25	|	|	PROPN
ma-136	354	26	→	→	SYM
ma-136	354	27	1−.	1−.	NOUN
ma-136	354	28	then	then	ADV
ma-136	354	29	,	,	PUNCT
ma-136	354	30	by	by	ADP
ma-136	354	31	(	(	PUNCT
ma-136	354	32	3.5	3.5	NUM
ma-136	354	33	)	)	PUNCT
ma-136	354	34	and	and	CCONJ
ma-136	354	35	combining	combine	VERB
ma-136	354	36	with	with	ADP
ma-136	354	37	lemma	lemma	PROPN
ma-136	354	38	2.3	2.3	NUM
ma-136	354	39	,	,	PUNCT
ma-136	354	40	weget	weget	VERB
ma-136	354	41	for	for	ADP
ma-136	354	42	all	all	PRON
ma-136	354	43	r	r	NOUN
ma-136	354	44	=	=	PUNCT
ma-136	354	45	|z	|z	PROPN
ma-136	354	46	|	|	ADV
ma-136	354	47	∈	∈	PROPN
ma-136	354	48	h1	h1	PROPN
ma-136	354	49	exp	exp	X
ma-136	354	50	(	(	PUNCT
ma-136	354	51	(	(	PUNCT
ma-136	354	52	1−	1−	NUM
ma-136	354	53	o(1	o(1	NOUN
ma-136	354	54	)	)	PUNCT
ma-136	354	55	)	)	PUNCT
ma-136	355	1	expp−1	expp−1	NOUN
ma-136	355	2	{	{	PUNCT
ma-136	355	3	γ	γ	X
ma-136	355	4	(	(	PUNCT
ma-136	355	5	logq−1	logq−1	X
ma-136	355	6	(	(	PUNCT
ma-136	355	7	1	1	NUM
ma-136	355	8	1−	1−	NUM
ma-136	355	9	r	r	NOUN
ma-136	355	10	)	)	PUNCT
ma-136	355	11	)	)	PUNCT
ma-136	355	12	µ	µ	X
ma-136	355	13	}	}	PUNCT
ma-136	355	14	)	)	PUNCT
ma-136	355	15	≤	≤	PUNCT
ma-136	356	1	k	k	X
ma-136	356	2	(	(	PUNCT
ma-136	356	3	1	1	NUM
ma-136	356	4	1−	1−	NUM
ma-136	356	5	s	s	X
ma-136	356	6	(	(	PUNCT
ma-136	356	7	r	r	NOUN
ma-136	356	8	)	)	PUNCT
ma-136	356	9	)	)	PUNCT
ma-136	356	10	k(2+ε	k(2+ε	PROPN
ma-136	356	11	)	)	PUNCT
ma-136	357	1	t	t	PROPN
ma-136	357	2	k	k	PROPN
ma-136	357	3	(	(	PUNCT
ma-136	357	4	s1	s1	NOUN
ma-136	357	5	(	(	PUNCT
ma-136	357	6	r	r	NOUN
ma-136	357	7	)	)	PUNCT
ma-136	357	8	,	,	PUNCT
ma-136	357	9	f	f	PROPN
ma-136	357	10	)	)	PUNCT
ma-136	357	11	,	,	PUNCT
ma-136	357	12	(	(	PUNCT
ma-136	357	13	3.6	3.6	NUM
ma-136	357	14	)	)	PUNCT
ma-136	357	15	where	where	SCONJ
ma-136	357	16	s1	s1	NOUN
ma-136	357	17	(	(	PUNCT
ma-136	357	18	r	r	NOUN
ma-136	357	19	)	)	PUNCT
ma-136	357	20	=	=	SYM
ma-136	357	21	1	1	NUM
ma-136	357	22	−	−	PROPN
ma-136	357	23	d2	d2	PROPN
ma-136	357	24	(	(	PUNCT
ma-136	357	25	1−	1−	NUM
ma-136	357	26	r	r	NOUN
ma-136	357	27	)	)	PUNCT
ma-136	357	28	with	with	ADP
ma-136	357	29	d	d	PROPN
ma-136	357	30	∈	∈	PROPN
ma-136	357	31	(	(	PUNCT
ma-136	357	32	0	0	NUM
ma-136	357	33	,	,	PUNCT
ma-136	357	34	1	1	NUM
ma-136	357	35	)	)	PUNCT
ma-136	357	36	.	.	PUNCT
ma-136	358	1	therefore	therefore	ADV
ma-136	358	2	,	,	PUNCT
ma-136	358	3	from	from	ADP
ma-136	358	4	(	(	PUNCT
ma-136	358	5	3.6	3.6	NUM
ma-136	358	6	)	)	PUNCT
ma-136	358	7	we	we	PRON
ma-136	358	8	obtain	obtain	VERB
ma-136	358	9	σ[p	σ[p	NOUN
ma-136	358	10	,	,	PUNCT
ma-136	358	11	q	q	X
ma-136	358	12	]	]	X
ma-136	358	13	(	(	PUNCT
ma-136	358	14	f	f	X
ma-136	358	15	)	)	PUNCT
ma-136	358	16	=	=	SYM
ma-136	358	17	σm,[p	σm,[p	NOUN
ma-136	358	18	,	,	PUNCT
ma-136	358	19	q	q	X
ma-136	358	20	]	]	X
ma-136	358	21	(	(	PUNCT
ma-136	358	22	f	f	X
ma-136	358	23	)	)	PUNCT
ma-136	359	1	=	=	NOUN
ma-136	359	2	∞	∞	NOUN
ma-136	359	3	and	and	CCONJ
ma-136	359	4	σ[p+1,q	σ[p+1,q	NOUN
ma-136	359	5	]	]	PUNCT
ma-136	359	6	(	(	PUNCT
ma-136	359	7	f	f	X
ma-136	359	8	)	)	PUNCT
ma-136	359	9	=	=	SYM
ma-136	360	1	σm,[p+1,q	σm,[p+1,q	X
ma-136	360	2	]	]	PUNCT
ma-136	360	3	(	(	PUNCT
ma-136	360	4	f	f	X
ma-136	360	5	)	)	PUNCT
ma-136	361	1	=	=	SYM
ma-136	361	2	lim	lim	PROPN
ma-136	361	3	sup	sup	PROPN
ma-136	361	4	s1(r)→1−	s1(r)→1−	PROPN
ma-136	361	5	log+p+1	log+p+1	PROPN
ma-136	361	6	t	t	PROPN
ma-136	361	7	(	(	PUNCT
ma-136	361	8	s1	s1	PROPN
ma-136	361	9	(	(	PUNCT
ma-136	361	10	r	r	NOUN
ma-136	361	11	)	)	PUNCT
ma-136	361	12	,	,	PUNCT
ma-136	361	13	f	f	X
ma-136	361	14	)	)	PUNCT
ma-136	361	15	logq	logq	NOUN
ma-136	361	16	(	(	PUNCT
ma-136	361	17	1	1	NUM
ma-136	361	18	1−s1(r	1−s1(r	NUM
ma-136	361	19	)	)	PUNCT
ma-136	361	20	)	)	PUNCT
ma-136	361	21	≥	≥	PROPN
ma-136	361	22	µ.	µ.	NOUN
ma-136	361	23	(	(	PUNCT
ma-136	361	24	3.7	3.7	NUM
ma-136	361	25	)	)	PUNCT
ma-136	361	26	by	by	ADP
ma-136	361	27	lemma	lemma	PROPN
ma-136	361	28	2.4	2.4	NUM
ma-136	361	29	,	,	PUNCT
ma-136	361	30	we	we	PRON
ma-136	361	31	get	get	VERB
ma-136	361	32	σ[p+1,q	σ[p+1,q	NOUN
ma-136	361	33	]	]	PUNCT
ma-136	361	34	(	(	PUNCT
ma-136	361	35	f	f	X
ma-136	361	36	)	)	PUNCT
ma-136	361	37	=	=	SYM
ma-136	362	1	σm,[p+1,q	σm,[p+1,q	X
ma-136	362	2	]	]	PUNCT
ma-136	362	3	(	(	PUNCT
ma-136	362	4	f	f	PROPN
ma-136	362	5	)	)	PUNCT
ma-136	362	6	≤	≤	PROPN
ma-136	362	7	max	max	PROPN
ma-136	362	8	{	{	PUNCT
ma-136	362	9	σm,[p	σm,[p	PROPN
ma-136	362	10	,	,	PUNCT
ma-136	362	11	q	q	X
ma-136	362	12	]	]	X
ma-136	362	13	(	(	PUNCT
ma-136	362	14	ai	ai	PROPN
ma-136	362	15	)	)	PUNCT
ma-136	362	16	:	:	PUNCT
ma-136	362	17	i	i	NOUN
ma-136	362	18	=	=	NOUN
ma-136	362	19	0	0	NUM
ma-136	362	20	,	,	PUNCT
ma-136	362	21	1	1	NUM
ma-136	362	22	,	,	PUNCT
ma-136	362	23	...	...	PUNCT
ma-136	362	24	,	,	PUNCT
ma-136	362	25	k	k	PROPN
ma-136	362	26	−	−	PROPN
ma-136	362	27	1	1	X
ma-136	362	28	}	}	PUNCT
ma-136	362	29	=	=	SYM
ma-136	362	30	σm,[p	σm,[p	NOUN
ma-136	362	31	,	,	PUNCT
ma-136	362	32	q	q	X
ma-136	362	33	]	]	X
ma-136	362	34	(	(	PUNCT
ma-136	362	35	a0	a0	NOUN
ma-136	362	36	)	)	PUNCT
ma-136	362	37	=	=	SYM
ma-136	362	38	µ.	µ.	NOUN
ma-136	362	39	(	(	PUNCT
ma-136	362	40	3.8)therefore	3.8)therefore	NUM
ma-136	362	41	,	,	PUNCT
ma-136	362	42	by	by	ADP
ma-136	362	43	(	(	PUNCT
ma-136	362	44	3.7	3.7	NUM
ma-136	362	45	)	)	PUNCT
ma-136	362	46	and	and	CCONJ
ma-136	362	47	(	(	PUNCT
ma-136	362	48	3.8	3.8	NUM
ma-136	362	49	)	)	PUNCT
ma-136	362	50	,	,	PUNCT
ma-136	362	51	we	we	PRON
ma-136	362	52	obtain	obtain	VERB
ma-136	362	53	σ[p	σ[p	NOUN
ma-136	362	54	,	,	PUNCT
ma-136	362	55	q	q	X
ma-136	362	56	]	]	X
ma-136	362	57	(	(	PUNCT
ma-136	362	58	f	f	X
ma-136	362	59	)	)	PUNCT
ma-136	362	60	=	=	SYM
ma-136	362	61	σm,[p	σm,[p	NOUN
ma-136	362	62	,	,	PUNCT
ma-136	362	63	q	q	X
ma-136	362	64	]	]	X
ma-136	362	65	(	(	PUNCT
ma-136	362	66	f	f	X
ma-136	362	67	)	)	PUNCT
ma-136	362	68	=	=	NOUN
ma-136	362	69	∞	∞	NOUN
ma-136	362	70	and	and	CCONJ
ma-136	362	71	σ[p+1,q	σ[p+1,q	NOUN
ma-136	362	72	]	]	PUNCT
ma-136	362	73	(	(	PUNCT
ma-136	362	74	f	f	X
ma-136	362	75	)	)	PUNCT
ma-136	362	76	=	=	SYM
ma-136	363	1	σm,[p+1,q	σm,[p+1,q	X
ma-136	363	2	]	]	PUNCT
ma-136	363	3	(	(	PUNCT
ma-136	363	4	f	f	X
ma-136	363	5	)	)	PUNCT
ma-136	363	6	=	=	SYM
ma-136	363	7	σm,[p	σm,[p	NOUN
ma-136	363	8	,	,	PUNCT
ma-136	363	9	q	q	X
ma-136	363	10	]	]	X
ma-136	363	11	(	(	PUNCT
ma-136	363	12	a0	a0	NOUN
ma-136	363	13	)	)	PUNCT
ma-136	363	14	=	=	PUNCT
ma-136	363	15	µ.	µ.	NOUN
ma-136	363	16	proof	proof	NOUN
ma-136	363	17	of	of	ADP
ma-136	363	18	theorem	theorem	ADJ
ma-136	363	19	1.2	1.2	NUM
ma-136	363	20	.	.	PUNCT
ma-136	363	21	set	set	VERB
ma-136	363	22	α0	α0	PROPN
ma-136	363	23	=	=	SYM
ma-136	363	24	lim	lim	PROPN
ma-136	363	25	inf	inf	PROPN
ma-136	363	26	|z	|z	PROPN
ma-136	363	27	|→1−,z∈h	|→1−,z∈h	PROPN
ma-136	363	28	logp	logp	NOUN
ma-136	363	29	|a0	|a0	PROPN
ma-136	364	1	(	(	PUNCT
ma-136	364	2	z)|	z)|	X
ma-136	364	3	(	(	PUNCT
ma-136	364	4	logq−1	logq−1	X
ma-136	364	5	(	(	PUNCT
ma-136	364	6	1	1	NUM
ma-136	364	7	1−|z	1−|z	NUM
ma-136	364	8	|	|	NOUN
ma-136	364	9	)	)	PUNCT
ma-136	364	10	)	)	PUNCT
ma-136	364	11	µ	µ	X
ma-136	364	12	,	,	PUNCT
ma-136	364	13	αi	αi	VERB
ma-136	365	1	=	=	SYM
ma-136	365	2	lim	lim	PROPN
ma-136	365	3	sup	sup	PROPN
ma-136	365	4	|z	|z	PROPN
ma-136	365	5	|→1−,z∈h	|→1−,z∈h	PROPN
ma-136	365	6	logp	logp	NOUN
ma-136	365	7	|ai	|ai	NUM
ma-136	365	8	(	(	PUNCT
ma-136	365	9	z)|	z)|	X
ma-136	365	10	(	(	PUNCT
ma-136	365	11	logq−1	logq−1	X
ma-136	365	12	(	(	PUNCT
ma-136	365	13	1	1	NUM
ma-136	365	14	1−|z	1−|z	NUM
ma-136	365	15	|	|	NOUN
ma-136	365	16	)	)	PUNCT
ma-136	365	17	)	)	PUNCT
ma-136	365	18	µ	µ	X
ma-136	365	19	,	,	PUNCT
ma-136	365	20	(	(	PUNCT
ma-136	365	21	i	i	NOUN
ma-136	365	22	=	=	NOUN
ma-136	365	23	1	1	NUM
ma-136	365	24	,	,	PUNCT
ma-136	365	25	2	2	NUM
ma-136	365	26	,	,	PUNCT
ma-136	365	27	...	...	PUNCT
ma-136	365	28	,	,	PUNCT
ma-136	365	29	k	k	PROPN
ma-136	365	30	−	−	PROPN
ma-136	365	31	1	1	NUM
ma-136	365	32	)	)	PUNCT
ma-136	365	33	.	.	PUNCT
ma-136	366	1	https://doi.org/10.28924/ada/ma.3.10	https://doi.org/10.28924/ada/ma.3.10	ADV
ma-136	366	2	eur	eur	PROPN
ma-136	366	3	.	.	PUNCT
ma-136	367	1	j.	j.	PROPN
ma-136	367	2	math	math	PROPN
ma-136	367	3	.	.	PUNCT
ma-136	368	1	anal	anal	PROPN
ma-136	368	2	.	.	PUNCT
ma-136	369	1	10.28924	10.28924	NUM
ma-136	369	2	/	/	SYM
ma-136	369	3	ada	ada	NOUN
ma-136	369	4	/	/	PROPN
ma-136	369	5	ma.3.10	ma.3.10	ADJ
ma-136	369	6	14by	14by	NOUN
ma-136	369	7	(	(	PUNCT
ma-136	369	8	1.5	1.5	NUM
ma-136	369	9	)	)	PUNCT
ma-136	369	10	,	,	PUNCT
ma-136	369	11	there	there	PRON
ma-136	369	12	exist	exist	VERB
ma-136	369	13	real	real	ADJ
ma-136	369	14	numbers	number	NOUN
ma-136	369	15	α	α	PRON
ma-136	369	16	,	,	PUNCT
ma-136	369	17	γ	γ	PROPN
ma-136	369	18	such	such	ADJ
ma-136	369	19	that	that	SCONJ
ma-136	369	20	αi	αi	VERB
ma-136	369	21	<	<	X
ma-136	369	22	α	α	X
ma-136	369	23	<	<	X
ma-136	369	24	γ	γ	X
ma-136	369	25	<	<	X
ma-136	369	26	α0	α0	PROPN
ma-136	369	27	,	,	PUNCT
ma-136	369	28	i	i	NOUN
ma-136	369	29	=	=	NOUN
ma-136	369	30	1	1	NUM
ma-136	369	31	,	,	PUNCT
ma-136	369	32	2	2	NUM
ma-136	369	33	,	,	PUNCT
ma-136	369	34	...	...	PUNCT
ma-136	369	35	,	,	PUNCT
ma-136	370	1	k	k	PROPN
ma-136	370	2	−	−	PROPN
ma-136	371	1	1	1	X
ma-136	371	2	.	.	PUNCT
ma-136	371	3	it	it	PRON
ma-136	371	4	yields	yield	VERB
ma-136	371	5	logp	logp	ADV
ma-136	371	6	|ai	|ai	NUM
ma-136	371	7	(	(	PUNCT
ma-136	371	8	z)|	z)|	X
ma-136	371	9	(	(	PUNCT
ma-136	371	10	logq−1	logq−1	X
ma-136	371	11	(	(	PUNCT
ma-136	371	12	1	1	NUM
ma-136	371	13	1−|z	1−|z	NUM
ma-136	371	14	|	|	NOUN
ma-136	371	15	)	)	PUNCT
ma-136	371	16	)	)	PUNCT
ma-136	371	17	µ	µ	X
ma-136	371	18	<	<	X
ma-136	371	19	α	α	X
ma-136	371	20	<	<	X
ma-136	371	21	γ	γ	X
ma-136	371	22	<	<	X
ma-136	371	23	logp	logp	NOUN
ma-136	371	24	|a0	|a0	PROPN
ma-136	371	25	(	(	PUNCT
ma-136	371	26	z)|	z)|	X
ma-136	371	27	(	(	PUNCT
ma-136	371	28	logq−1	logq−1	X
ma-136	371	29	(	(	PUNCT
ma-136	371	30	1	1	NUM
ma-136	371	31	1−|z	1−|z	NUM
ma-136	371	32	|	|	NOUN
ma-136	371	33	)	)	PUNCT
ma-136	371	34	)	)	PUNCT
ma-136	371	35	µ	µ	X
ma-136	371	36	as	as	ADP
ma-136	371	37	|z	|z	PROPN
ma-136	371	38	|	|	PROPN
ma-136	371	39	→	→	SYM
ma-136	371	40	1−	1−	NUM
ma-136	371	41	for	for	ADP
ma-136	371	42	z	z	PROPN
ma-136	371	43	∈	∈	PROPN
ma-136	371	44	h.	h.	PROPN
ma-136	371	45	hence	hence	ADV
ma-136	371	46	,	,	PUNCT
ma-136	371	47	we	we	PRON
ma-136	371	48	have	have	VERB
ma-136	371	49	(	(	PUNCT
ma-136	371	50	3.4	3.4	NUM
ma-136	371	51	)	)	PUNCT
ma-136	371	52	as	as	ADP
ma-136	371	53	|z	|z	PROPN
ma-136	371	54	|	|	PROPN
ma-136	371	55	→	→	SYM
ma-136	371	56	1−	1−	NUM
ma-136	371	57	for	for	ADP
ma-136	371	58	z	z	PROPN
ma-136	371	59	∈	∈	PROPN
ma-136	371	60	h.	h.	NOUN
ma-136	371	61	then	then	ADV
ma-136	371	62	,	,	PUNCT
ma-136	371	63	by	by	ADP
ma-136	371	64	using	use	VERB
ma-136	371	65	the	the	DET
ma-136	371	66	sameproof	sameproof	NOUN
ma-136	371	67	of	of	ADP
ma-136	371	68	theorem	theorem	ADJ
ma-136	371	69	1.1	1.1	NUM
ma-136	371	70	,	,	PUNCT
ma-136	371	71	we	we	PRON
ma-136	371	72	get	get	VERB
ma-136	371	73	σ[p	σ[p	NOUN
ma-136	371	74	,	,	PUNCT
ma-136	371	75	q	q	X
ma-136	371	76	]	]	X
ma-136	371	77	(	(	PUNCT
ma-136	371	78	f	f	X
ma-136	371	79	)	)	PUNCT
ma-136	371	80	=	=	SYM
ma-136	371	81	σm,[p	σm,[p	NOUN
ma-136	371	82	,	,	PUNCT
ma-136	371	83	q	q	X
ma-136	371	84	]	]	X
ma-136	371	85	(	(	PUNCT
ma-136	371	86	f	f	X
ma-136	371	87	)	)	PUNCT
ma-136	372	1	=	=	NOUN
ma-136	372	2	∞	∞	NOUN
ma-136	372	3	and	and	CCONJ
ma-136	372	4	σ[p+1,q	σ[p+1,q	NOUN
ma-136	372	5	]	]	PUNCT
ma-136	372	6	(	(	PUNCT
ma-136	372	7	f	f	X
ma-136	372	8	)	)	PUNCT
ma-136	372	9	=	=	SYM
ma-136	373	1	σm,[p+1,q	σm,[p+1,q	X
ma-136	373	2	]	]	PUNCT
ma-136	373	3	(	(	PUNCT
ma-136	373	4	f	f	PROPN
ma-136	373	5	)	)	PUNCT
ma-136	373	6	≥	≥	PROPN
ma-136	373	7	µ	µ	PROPN
ma-136	373	8	and	and	CCONJ
ma-136	373	9	by	by	ADP
ma-136	373	10	lemma	lemma	PROPN
ma-136	373	11	2.4	2.4	NUM
ma-136	373	12	we	we	PRON
ma-136	373	13	obtain	obtain	VERB
ma-136	373	14	the	the	DET
ma-136	373	15	conclusion	conclusion	NOUN
ma-136	373	16	of	of	ADP
ma-136	373	17	theorem	theorem	ADJ
ma-136	373	18	1.2	1.2	NUM
ma-136	373	19	.	.	PUNCT
ma-136	374	1	proof	proof	NOUN
ma-136	374	2	of	of	ADP
ma-136	374	3	theorem	theorem	NOUN
ma-136	374	4	1.3	1.3	NUM
ma-136	374	5	.	.	PUNCT
ma-136	374	6	suppose	suppose	VERB
ma-136	374	7	that	that	SCONJ
ma-136	374	8	every	every	DET
ma-136	374	9	solution	solution	NOUN
ma-136	374	10	f	f	PROPN
ma-136	374	11	of	of	ADP
ma-136	374	12	equation	equation	NOUN
ma-136	374	13	(	(	PUNCT
ma-136	374	14	1.1	1.1	NUM
ma-136	374	15	)	)	PUNCT
ma-136	374	16	not	not	PART
ma-136	374	17	being	be	AUX
ma-136	374	18	identically	identically	ADV
ma-136	374	19	equalto	equalto	NOUN
ma-136	374	20	0	0	NUM
ma-136	374	21	.	.	PUNCT
ma-136	375	1	by	by	ADP
ma-136	375	2	(	(	PUNCT
ma-136	375	3	1.1	1.1	NUM
ma-136	375	4	)	)	PUNCT
ma-136	375	5	,	,	PUNCT
ma-136	375	6	we	we	PRON
ma-136	375	7	can	can	AUX
ma-136	375	8	write	write	VERB
ma-136	375	9	−	−	PROPN
ma-136	375	10	a0	a0	PROPN
ma-136	375	11	(	(	PUNCT
ma-136	375	12	z	z	NOUN
ma-136	375	13	)	)	PUNCT
ma-136	376	1	=	=	SYM
ma-136	376	2	f	f	PROPN
ma-136	376	3	(	(	PUNCT
ma-136	376	4	k)(z	k)(z	NOUN
ma-136	376	5	)	)	PUNCT
ma-136	376	6	f	f	NOUN
ma-136	376	7	(	(	PUNCT
ma-136	376	8	z	z	NOUN
ma-136	376	9	)	)	PUNCT
ma-136	377	1	+	+	CCONJ
ma-136	377	2	ak−1	ak−1	ADV
ma-136	377	3	(	(	PUNCT
ma-136	377	4	z	z	NOUN
ma-136	377	5	)	)	PUNCT
ma-136	377	6	f	f	PROPN
ma-136	377	7	(	(	PUNCT
ma-136	377	8	k−1)(z	k−1)(z	PROPN
ma-136	377	9	)	)	PUNCT
ma-136	377	10	f	f	PROPN
ma-136	377	11	(	(	PUNCT
ma-136	377	12	z	z	NOUN
ma-136	377	13	)	)	PUNCT
ma-136	377	14	+	+	CCONJ
ma-136	377	15	·	·	PUNCT
ma-136	377	16	·	·	PUNCT
ma-136	377	17	·	·	PUNCT
ma-136	378	1	+	+	NUM
ma-136	378	2	a1	a1	NOUN
ma-136	378	3	(	(	PUNCT
ma-136	378	4	z	z	NOUN
ma-136	378	5	)	)	PUNCT
ma-136	378	6	f	f	PROPN
ma-136	378	7	′(z	′(z	NOUN
ma-136	378	8	)	)	PUNCT
ma-136	378	9	f	f	PROPN
ma-136	378	10	(	(	PUNCT
ma-136	378	11	z	z	NOUN
ma-136	378	12	)	)	PUNCT
ma-136	378	13	.	.	PUNCT
ma-136	379	1	(	(	PUNCT
ma-136	379	2	3.9	3.9	NUM
ma-136	379	3	)	)	PUNCT
ma-136	379	4	from	from	ADP
ma-136	379	5	(	(	PUNCT
ma-136	379	6	3.9	3.9	NUM
ma-136	379	7	)	)	PUNCT
ma-136	379	8	,	,	PUNCT
ma-136	379	9	we	we	PRON
ma-136	379	10	obtain	obtain	VERB
ma-136	379	11	t	t	NOUN
ma-136	379	12	(	(	PUNCT
ma-136	379	13	r	r	NOUN
ma-136	379	14	,	,	PUNCT
ma-136	379	15	a0	a0	NOUN
ma-136	379	16	)	)	PUNCT
ma-136	379	17	=	=	SYM
ma-136	379	18	m(r	m(r	PROPN
ma-136	379	19	,	,	PUNCT
ma-136	379	20	a0	a0	NOUN
ma-136	379	21	)	)	PUNCT
ma-136	379	22	≤	≤	PUNCT
ma-136	380	1	k−1∑	k−1∑	PROPN
ma-136	380	2	i=1	i=1	PROPN
ma-136	380	3	m(r	m(r	PROPN
ma-136	380	4	,	,	PUNCT
ma-136	380	5	ai	ai	VERB
ma-136	380	6	)	)	PUNCT
ma-136	380	7	+	+	CCONJ
ma-136	380	8	k∑	k∑	VERB
ma-136	380	9	i=1	i=1	INTJ
ma-136	380	10	m	m	VERB
ma-136	380	11	(	(	PUNCT
ma-136	380	12	r	r	NOUN
ma-136	380	13	,	,	PUNCT
ma-136	380	14	f	f	PROPN
ma-136	380	15	(	(	PUNCT
ma-136	380	16	i	i	NOUN
ma-136	380	17	)	)	PUNCT
ma-136	380	18	f	f	PROPN
ma-136	380	19	)	)	PUNCT
ma-136	381	1	+	+	NOUN
ma-136	381	2	o(1	o(1	NOUN
ma-136	381	3	)	)	PUNCT
ma-136	381	4	=	=	PUNCT
ma-136	381	5	k−1∑	k−1∑	PROPN
ma-136	381	6	i=1	i=1	PROPN
ma-136	381	7	t	t	PROPN
ma-136	381	8	(	(	PUNCT
ma-136	381	9	r	r	NOUN
ma-136	381	10	,	,	PUNCT
ma-136	381	11	ai	ai	VERB
ma-136	381	12	)	)	PUNCT
ma-136	381	13	+	+	CCONJ
ma-136	381	14	k∑	k∑	VERB
ma-136	381	15	i=1	i=1	INTJ
ma-136	381	16	m	m	VERB
ma-136	381	17	(	(	PUNCT
ma-136	381	18	r	r	NOUN
ma-136	381	19	,	,	PUNCT
ma-136	381	20	f	f	PROPN
ma-136	381	21	(	(	PUNCT
ma-136	381	22	i	i	NOUN
ma-136	381	23	)	)	PUNCT
ma-136	381	24	f	f	PROPN
ma-136	381	25	)	)	PUNCT
ma-136	382	1	+	+	NOUN
ma-136	382	2	o(1	o(1	NOUN
ma-136	382	3	)	)	PUNCT
ma-136	382	4	.	.	PUNCT
ma-136	383	1	(	(	PUNCT
ma-136	383	2	3.10	3.10	NUM
ma-136	383	3	)	)	PUNCT
ma-136	383	4	if	if	SCONJ
ma-136	383	5	p	p	PROPN
ma-136	383	6	≥	≥	PUNCT
ma-136	383	7	q	q	X
ma-136	383	8	≥	≥	NUM
ma-136	383	9	2	2	NUM
ma-136	383	10	,	,	PUNCT
ma-136	383	11	then	then	ADV
ma-136	383	12	by	by	ADP
ma-136	383	13	(	(	PUNCT
ma-136	383	14	1.6	1.6	NUM
ma-136	383	15	)	)	PUNCT
ma-136	383	16	,	,	PUNCT
ma-136	383	17	we	we	PRON
ma-136	383	18	know	know	VERB
ma-136	383	19	that	that	SCONJ
ma-136	383	20	∃γ	∃γ	NOUN
ma-136	383	21	∈	∈	NOUN
ma-136	383	22	r	r	NOUN
ma-136	383	23	:	:	PUNCT
ma-136	383	24	lim	lim	PROPN
ma-136	383	25	inf	inf	PROPN
ma-136	383	26	|z	|z	PROPN
ma-136	383	27	|→1−,z∈h	|→1−,z∈h	PROPN
ma-136	383	28	logp−1	logp−1	PROPN
ma-136	383	29	t	t	PROPN
ma-136	383	30	(	(	PUNCT
ma-136	383	31	r	r	PROPN
ma-136	383	32	,	,	PUNCT
ma-136	383	33	a0	a0	NOUN
ma-136	383	34	)	)	PUNCT
ma-136	383	35	(	(	PUNCT
ma-136	383	36	logq−1	logq−1	X
ma-136	383	37	(	(	PUNCT
ma-136	383	38	1	1	NUM
ma-136	383	39	1−|z	1−|z	NUM
ma-136	383	40	|	|	NOUN
ma-136	383	41	)	)	PUNCT
ma-136	383	42	)	)	PUNCT
ma-136	383	43	µ	µ	X
ma-136	383	44	>	>	X
ma-136	383	45	γ	γ	X
ma-136	383	46	>	>	X
ma-136	383	47	α	α	PROPN
ma-136	383	48	.	.	PUNCT
ma-136	384	1	obviously	obviously	ADV
ma-136	384	2	logp−1	logp−1	PROPN
ma-136	384	3	t	t	PROPN
ma-136	384	4	(	(	PUNCT
ma-136	384	5	r	r	PROPN
ma-136	384	6	,	,	PUNCT
ma-136	384	7	a0	a0	NOUN
ma-136	384	8	)	)	PUNCT
ma-136	384	9	(	(	PUNCT
ma-136	384	10	logq−1	logq−1	X
ma-136	384	11	(	(	PUNCT
ma-136	384	12	1	1	NUM
ma-136	384	13	1−|z	1−|z	NUM
ma-136	384	14	|	|	NOUN
ma-136	384	15	)	)	PUNCT
ma-136	384	16	)	)	PUNCT
ma-136	384	17	µ	µ	X
ma-136	384	18	>	>	X
ma-136	384	19	γ	γ	X
ma-136	384	20	>	>	X
ma-136	384	21	α	α	PROPN
ma-136	384	22	≥	≥	NOUN
ma-136	384	23	0	0	NUM
ma-136	384	24	(	(	PUNCT
ma-136	384	25	3.11	3.11	NUM
ma-136	384	26	)	)	PUNCT
ma-136	384	27	as	as	ADP
ma-136	384	28	|z	|z	PROPN
ma-136	384	29	|	|	PROPN
ma-136	384	30	→	→	SYM
ma-136	384	31	1−	1−	NUM
ma-136	384	32	for	for	ADP
ma-136	384	33	z	z	PROPN
ma-136	384	34	∈	∈	PROPN
ma-136	384	35	h.	h.	PROPN
ma-136	384	36	by	by	ADP
ma-136	384	37	(	(	PUNCT
ma-136	384	38	1.7	1.7	NUM
ma-136	384	39	)	)	PUNCT
ma-136	384	40	and	and	CCONJ
ma-136	384	41	(	(	PUNCT
ma-136	384	42	3.11	3.11	NUM
ma-136	384	43	)	)	PUNCT
ma-136	384	44	,	,	PUNCT
ma-136	384	45	we	we	PRON
ma-136	384	46	obtain	obtain	VERB
ma-136	384	47	t	t	NOUN
ma-136	384	48	(	(	PUNCT
ma-136	384	49	r	r	NOUN
ma-136	384	50	,	,	PUNCT
ma-136	384	51	a0	a0	NOUN
ma-136	384	52	)	)	PUNCT
ma-136	384	53	>	>	X
ma-136	385	1	expp−1	expp−1	NOUN
ma-136	385	2	{	{	PUNCT
ma-136	385	3	γ	γ	X
ma-136	385	4	(	(	PUNCT
ma-136	385	5	logq−1	logq−1	X
ma-136	385	6	(	(	PUNCT
ma-136	385	7	1	1	NUM
ma-136	385	8	1−	1−	NUM
ma-136	385	9	|z	|z	NOUN
ma-136	385	10	|	|	ADV
ma-136	385	11	)	)	PUNCT
ma-136	385	12	)	)	PUNCT
ma-136	385	13	µ	µ	X
ma-136	385	14	}	}	PUNCT
ma-136	385	15	>	>	X
ma-136	385	16	expp−1	expp−1	NOUN
ma-136	385	17	{	{	PUNCT
ma-136	385	18	α	α	PROPN
ma-136	385	19	(	(	PUNCT
ma-136	385	20	logq−1	logq−1	X
ma-136	385	21	(	(	PUNCT
ma-136	385	22	1	1	NUM
ma-136	385	23	1−	1−	NUM
ma-136	385	24	|z	|z	NOUN
ma-136	385	25	|	|	ADV
ma-136	385	26	)	)	PUNCT
ma-136	385	27	)	)	PUNCT
ma-136	385	28	µ	µ	X
ma-136	385	29	}	}	PUNCT
ma-136	385	30	≥	≥	NOUN
ma-136	385	31	t	t	NOUN
ma-136	385	32	(	(	PUNCT
ma-136	385	33	r	r	NOUN
ma-136	385	34	,	,	PUNCT
ma-136	385	35	ai	ai	NOUN
ma-136	385	36	)	)	PUNCT
ma-136	385	37	,	,	PUNCT
ma-136	385	38	(	(	PUNCT
ma-136	385	39	i	i	NOUN
ma-136	385	40	=	=	NOUN
ma-136	385	41	1	1	NUM
ma-136	385	42	,	,	PUNCT
ma-136	385	43	2	2	NUM
ma-136	385	44	,	,	PUNCT
ma-136	385	45	...	...	PUNCT
ma-136	385	46	,	,	PUNCT
ma-136	385	47	k	k	PROPN
ma-136	386	1	−	−	PROPN
ma-136	386	2	1	1	NUM
ma-136	386	3	)	)	PUNCT
ma-136	386	4	(	(	PUNCT
ma-136	386	5	3.12	3.12	NUM
ma-136	386	6	)	)	PUNCT
ma-136	386	7	as	as	ADP
ma-136	386	8	|z	|z	PROPN
ma-136	386	9	|	|	PROPN
ma-136	386	10	→	→	SYM
ma-136	386	11	1−	1−	NUM
ma-136	386	12	for	for	ADP
ma-136	386	13	z	z	PROPN
ma-136	386	14	∈	∈	PROPN
ma-136	386	15	h.	h.	NOUN
ma-136	386	16	by	by	ADP
ma-136	386	17	applying	apply	VERB
ma-136	386	18	lemma	lemma	PROPN
ma-136	386	19	2.2	2.2	NUM
ma-136	386	20	and	and	CCONJ
ma-136	386	21	substituting	substitute	VERB
ma-136	386	22	(	(	PUNCT
ma-136	386	23	3.12	3.12	NUM
ma-136	386	24	)	)	PUNCT
ma-136	386	25	into	into	ADP
ma-136	386	26	(	(	PUNCT
ma-136	386	27	3.10	3.10	NUM
ma-136	386	28	)	)	PUNCT
ma-136	386	29	,	,	PUNCT
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ma-136	386	31	get	get	VERB
ma-136	386	32	expp−1	expp−1	NOUN
ma-136	386	33	{	{	PUNCT
ma-136	386	34	γ	γ	X
ma-136	386	35	(	(	PUNCT
ma-136	386	36	logq−1	logq−1	X
ma-136	386	37	(	(	PUNCT
ma-136	386	38	1	1	NUM
ma-136	386	39	1−	1−	NUM
ma-136	386	40	r	r	NOUN
ma-136	386	41	)	)	PUNCT
ma-136	386	42	)	)	PUNCT
ma-136	386	43	µ	µ	X
ma-136	386	44	}	}	PUNCT
ma-136	386	45	≤	≤	NOUN
ma-136	386	46	(	(	PUNCT
ma-136	386	47	k	k	NOUN
ma-136	386	48	−	−	PROPN
ma-136	386	49	1	1	X
ma-136	386	50	)	)	PUNCT
ma-136	386	51	expp−1	expp−1	NOUN
ma-136	386	52	{	{	PUNCT
ma-136	386	53	α	α	PROPN
ma-136	386	54	(	(	PUNCT
ma-136	386	55	logq−1	logq−1	X
ma-136	386	56	(	(	PUNCT
ma-136	386	57	1	1	NUM
ma-136	386	58	1−	1−	NUM
ma-136	386	59	r	r	NOUN
ma-136	386	60	)	)	PUNCT
ma-136	386	61	)	)	PUNCT
ma-136	386	62	µ	µ	X
ma-136	386	63	}	}	PUNCT
ma-136	386	64	+	+	NOUN
ma-136	386	65	o	o	X
ma-136	387	1	(	(	PUNCT
ma-136	387	2	log+	log+	PROPN
ma-136	387	3	t	t	X
ma-136	387	4	(	(	PUNCT
ma-136	387	5	r	r	NOUN
ma-136	387	6	,	,	PUNCT
ma-136	387	7	f	f	PROPN
ma-136	387	8	)	)	PUNCT
ma-136	388	1	+	+	CCONJ
ma-136	388	2	log	log	NOUN
ma-136	388	3	(	(	PUNCT
ma-136	388	4	1	1	NUM
ma-136	388	5	1−	1−	NUM
ma-136	388	6	r	r	NOUN
ma-136	388	7	)	)	PUNCT
ma-136	388	8	)	)	PUNCT
ma-136	388	9	https://doi.org/10.28924/ada/ma.3.10	https://doi.org/10.28924/ada/ma.3.10	ADV
ma-136	388	10	eur	eur	PROPN
ma-136	388	11	.	.	PUNCT
ma-136	389	1	j.	j.	PROPN
ma-136	389	2	math	math	PROPN
ma-136	389	3	.	.	PUNCT
ma-136	390	1	anal	anal	PROPN
ma-136	390	2	.	.	PUNCT
ma-136	391	1	10.28924	10.28924	NUM
ma-136	391	2	/	/	SYM
ma-136	391	3	ada	ada	NOUN
ma-136	391	4	/	/	SYM
ma-136	391	5	ma.3.10	ma.3.10	NOUN
ma-136	391	6	15for	15for	NOUN
ma-136	391	7	all	all	DET
ma-136	391	8	z	z	NOUN
ma-136	391	9	satisfying	satisfy	VERB
ma-136	391	10	|z	|z	NOUN
ma-136	392	1	|	|	ADV
ma-136	392	2	=	=	SYM
ma-136	392	3	r	r	NOUN
ma-136	392	4	∈	∈	NOUN
ma-136	392	5	h1\e2	h1\e2	PUNCT
ma-136	392	6	as	as	ADP
ma-136	392	7	|z	|z	PROPN
ma-136	392	8	|	|	ADV
ma-136	392	9	=	=	SYM
ma-136	392	10	r	r	NOUN
ma-136	392	11	→	→	SYM
ma-136	392	12	1−.	1−.	NUM
ma-136	392	13	noting	note	VERB
ma-136	392	14	that	that	SCONJ
ma-136	392	15	γ	γ	PROPN
ma-136	392	16	>	>	X
ma-136	392	17	α	α	PROPN
ma-136	392	18	,	,	PUNCT
ma-136	392	19	by	by	ADP
ma-136	392	20	the	the	DET
ma-136	392	21	last	last	ADJ
ma-136	392	22	inequality	inequality	NOUN
ma-136	392	23	,	,	PUNCT
ma-136	392	24	we	we	PRON
ma-136	392	25	have	have	VERB
ma-136	392	26	exp	exp	NOUN
ma-136	392	27	{	{	PUNCT
ma-136	392	28	(	(	PUNCT
ma-136	392	29	1−	1−	NUM
ma-136	392	30	o	o	NOUN
ma-136	392	31	(	(	PUNCT
ma-136	392	32	1	1	NUM
ma-136	392	33	)	)	PUNCT
ma-136	392	34	)	)	PUNCT
ma-136	393	1	expp−2	expp−2	PROPN
ma-136	393	2	{	{	PUNCT
ma-136	393	3	γ	γ	X
ma-136	393	4	(	(	PUNCT
ma-136	393	5	logq−1	logq−1	X
ma-136	393	6	(	(	PUNCT
ma-136	393	7	1	1	NUM
ma-136	393	8	1−	1−	NUM
ma-136	393	9	r	r	NOUN
ma-136	393	10	)	)	PUNCT
ma-136	393	11	)	)	PUNCT
ma-136	393	12	µ	µ	X
ma-136	393	13	}	}	PUNCT
ma-136	393	14	}	}	PUNCT
ma-136	393	15	≤	≤	NOUN
ma-136	393	16	o	o	NOUN
ma-136	394	1	(	(	PUNCT
ma-136	394	2	log+	log+	PROPN
ma-136	394	3	t	t	X
ma-136	394	4	(	(	PUNCT
ma-136	394	5	r	r	NOUN
ma-136	394	6	,	,	PUNCT
ma-136	394	7	f	f	PROPN
ma-136	394	8	)	)	PUNCT
ma-136	395	1	+	+	CCONJ
ma-136	395	2	log	log	NOUN
ma-136	395	3	(	(	PUNCT
ma-136	395	4	1	1	NUM
ma-136	395	5	1−	1−	NUM
ma-136	395	6	r	r	NOUN
ma-136	395	7	)	)	PUNCT
ma-136	395	8	)	)	PUNCT
ma-136	395	9	(	(	PUNCT
ma-136	395	10	3.13	3.13	NUM
ma-136	395	11	)	)	PUNCT
ma-136	395	12	for	for	ADP
ma-136	395	13	all	all	PRON
ma-136	395	14	z	z	NOUN
ma-136	395	15	satisfying	satisfy	VERB
ma-136	395	16	|z	|z	PROPN
ma-136	396	1	|	|	ADV
ma-136	396	2	=	=	SYM
ma-136	396	3	r	r	NOUN
ma-136	396	4	∈	∈	NOUN
ma-136	396	5	h1\e2	h1\e2	PUNCT
ma-136	396	6	as	as	ADP
ma-136	396	7	|z	|z	PROPN
ma-136	396	8	|	|	ADV
ma-136	396	9	=	=	SYM
ma-136	396	10	r	r	NOUN
ma-136	396	11	→	→	SYM
ma-136	396	12	1−.	1−.	PROPN
ma-136	396	13	therefore	therefore	ADV
ma-136	396	14	,	,	PUNCT
ma-136	396	15	from	from	ADP
ma-136	396	16	(	(	PUNCT
ma-136	396	17	3.13	3.13	NUM
ma-136	396	18	)	)	PUNCT
ma-136	396	19	we	we	PRON
ma-136	396	20	obtain	obtain	VERB
ma-136	396	21	σ[p	σ[p	NOUN
ma-136	396	22	,	,	PUNCT
ma-136	396	23	q	q	X
ma-136	396	24	]	]	X
ma-136	396	25	(	(	PUNCT
ma-136	396	26	f	f	X
ma-136	396	27	)	)	PUNCT
ma-136	396	28	=	=	SYM
ma-136	396	29	σm,[p	σm,[p	NOUN
ma-136	396	30	,	,	PUNCT
ma-136	396	31	q	q	X
ma-136	396	32	]	]	X
ma-136	396	33	(	(	PUNCT
ma-136	396	34	f	f	X
ma-136	396	35	)	)	PUNCT
ma-136	397	1	=	=	NOUN
ma-136	397	2	∞	∞	NOUN
ma-136	397	3	and	and	CCONJ
ma-136	397	4	σ[p+1,q	σ[p+1,q	NOUN
ma-136	397	5	]	]	PUNCT
ma-136	397	6	(	(	PUNCT
ma-136	397	7	f	f	X
ma-136	397	8	)	)	PUNCT
ma-136	397	9	=	=	SYM
ma-136	398	1	σm,[p+1,q	σm,[p+1,q	X
ma-136	398	2	]	]	PUNCT
ma-136	398	3	(	(	PUNCT
ma-136	398	4	f	f	PROPN
ma-136	398	5	)	)	PUNCT
ma-136	398	6	≥	≥	PROPN
ma-136	398	7	µ.	µ.	NOUN
ma-136	398	8	(	(	PUNCT
ma-136	398	9	3.14	3.14	NUM
ma-136	398	10	)	)	PUNCT
ma-136	398	11	by	by	ADP
ma-136	398	12	lemma	lemma	PROPN
ma-136	398	13	2.4	2.4	NUM
ma-136	398	14	,	,	PUNCT
ma-136	398	15	we	we	PRON
ma-136	398	16	get	get	VERB
ma-136	398	17	σ[p+1,q	σ[p+1,q	NOUN
ma-136	398	18	]	]	PUNCT
ma-136	398	19	(	(	PUNCT
ma-136	398	20	f	f	X
ma-136	398	21	)	)	PUNCT
ma-136	398	22	=	=	SYM
ma-136	399	1	σm,[p+1,q	σm,[p+1,q	X
ma-136	399	2	]	]	PUNCT
ma-136	399	3	(	(	PUNCT
ma-136	399	4	f	f	PROPN
ma-136	399	5	)	)	PUNCT
ma-136	399	6	≤	≤	PROPN
ma-136	399	7	max	max	PROPN
ma-136	399	8	{	{	PUNCT
ma-136	399	9	σm,[p	σm,[p	PROPN
ma-136	399	10	,	,	PUNCT
ma-136	399	11	q	q	X
ma-136	399	12	]	]	X
ma-136	399	13	(	(	PUNCT
ma-136	399	14	ai	ai	PROPN
ma-136	399	15	)	)	PUNCT
ma-136	399	16	:	:	PUNCT
ma-136	399	17	i	i	NOUN
ma-136	399	18	=	=	NOUN
ma-136	399	19	0	0	NUM
ma-136	399	20	,	,	PUNCT
ma-136	399	21	1	1	NUM
ma-136	399	22	,	,	PUNCT
ma-136	399	23	...	...	PUNCT
ma-136	399	24	,	,	PUNCT
ma-136	399	25	k	k	PROPN
ma-136	399	26	−	−	PROPN
ma-136	399	27	1	1	X
ma-136	399	28	}	}	PUNCT
ma-136	399	29	=	=	SYM
ma-136	399	30	σm,[p	σm,[p	NOUN
ma-136	399	31	,	,	PUNCT
ma-136	399	32	q	q	X
ma-136	399	33	]	]	X
ma-136	399	34	(	(	PUNCT
ma-136	399	35	a0	a0	NOUN
ma-136	399	36	)	)	PUNCT
ma-136	399	37	=	=	SYM
ma-136	399	38	µ.	µ.	NOUN
ma-136	399	39	(	(	PUNCT
ma-136	399	40	3.15)therefore	3.15)therefore	NUM
ma-136	399	41	,	,	PUNCT
ma-136	399	42	by	by	ADP
ma-136	399	43	(	(	PUNCT
ma-136	399	44	3.14	3.14	NUM
ma-136	399	45	)	)	PUNCT
ma-136	399	46	and	and	CCONJ
ma-136	399	47	(	(	PUNCT
ma-136	399	48	3.15	3.15	NUM
ma-136	399	49	)	)	PUNCT
ma-136	399	50	,	,	PUNCT
ma-136	399	51	we	we	PRON
ma-136	399	52	obtain	obtain	VERB
ma-136	399	53	σ[p	σ[p	NOUN
ma-136	399	54	,	,	PUNCT
ma-136	399	55	q	q	X
ma-136	399	56	]	]	X
ma-136	399	57	(	(	PUNCT
ma-136	399	58	f	f	X
ma-136	399	59	)	)	PUNCT
ma-136	399	60	=	=	SYM
ma-136	399	61	σm,[p	σm,[p	NOUN
ma-136	399	62	,	,	PUNCT
ma-136	399	63	q	q	X
ma-136	399	64	]	]	X
ma-136	399	65	(	(	PUNCT
ma-136	399	66	f	f	X
ma-136	399	67	)	)	PUNCT
ma-136	399	68	=	=	NOUN
ma-136	399	69	∞	∞	NOUN
ma-136	399	70	and	and	CCONJ
ma-136	399	71	σ[p+1,q	σ[p+1,q	NOUN
ma-136	399	72	]	]	PUNCT
ma-136	399	73	(	(	PUNCT
ma-136	399	74	f	f	X
ma-136	399	75	)	)	PUNCT
ma-136	399	76	=	=	SYM
ma-136	400	1	σm,[p+1,q	σm,[p+1,q	X
ma-136	400	2	]	]	PUNCT
ma-136	400	3	(	(	PUNCT
ma-136	400	4	f	f	X
ma-136	400	5	)	)	PUNCT
ma-136	400	6	=	=	PUNCT
ma-136	401	1	µ.	µ.	NOUN
ma-136	401	2	if	if	SCONJ
ma-136	401	3	p	p	NOUN
ma-136	401	4	=	=	X
ma-136	401	5	q	q	NOUN
ma-136	401	6	=	=	NOUN
ma-136	401	7	1	1	NUM
ma-136	401	8	,	,	PUNCT
ma-136	401	9	then	then	ADV
ma-136	401	10	by	by	ADP
ma-136	401	11	(	(	PUNCT
ma-136	401	12	1.8	1.8	NUM
ma-136	401	13	)	)	PUNCT
ma-136	401	14	,	,	PUNCT
ma-136	401	15	we	we	PRON
ma-136	401	16	know	know	VERB
ma-136	401	17	that	that	SCONJ
ma-136	401	18	∃γ	∃γ	NOUN
ma-136	401	19	∈	∈	NOUN
ma-136	401	20	r	r	NOUN
ma-136	401	21	:	:	PUNCT
ma-136	401	22	lim	lim	PROPN
ma-136	401	23	inf	inf	PROPN
ma-136	401	24	|z	|z	PROPN
ma-136	401	25	|→1−,z∈h	|→1−,z∈h	PROPN
ma-136	401	26	t	t	PROPN
ma-136	401	27	(	(	PUNCT
ma-136	401	28	r	r	PROPN
ma-136	401	29	,	,	PUNCT
ma-136	401	30	a0	a0	NOUN
ma-136	401	31	)	)	PUNCT
ma-136	401	32	(	(	PUNCT
ma-136	401	33	1	1	NUM
ma-136	401	34	1−|z	1−|z	NUM
ma-136	401	35	|	|	NOUN
ma-136	401	36	)	)	PUNCT
ma-136	401	37	µ	µ	X
ma-136	401	38	>	>	X
ma-136	401	39	γ	γ	X
ma-136	401	40	>	>	X
ma-136	402	1	(	(	PUNCT
ma-136	402	2	k	k	PROPN
ma-136	402	3	−	−	PROPN
ma-136	402	4	1)α	1)α	NUM
ma-136	402	5	.	.	PUNCT
ma-136	403	1	obviously	obviously	ADV
ma-136	403	2	t	t	PROPN
ma-136	403	3	(	(	PUNCT
ma-136	403	4	r	r	NOUN
ma-136	403	5	,	,	PUNCT
ma-136	403	6	a0	a0	NOUN
ma-136	403	7	)	)	PUNCT
ma-136	403	8	(	(	PUNCT
ma-136	403	9	1	1	NUM
ma-136	403	10	1−|z	1−|z	NUM
ma-136	403	11	|	|	NOUN
ma-136	403	12	)	)	PUNCT
ma-136	403	13	µ	µ	X
ma-136	403	14	>	>	X
ma-136	403	15	γ	γ	X
ma-136	403	16	>	>	X
ma-136	404	1	(	(	PUNCT
ma-136	404	2	k	k	PROPN
ma-136	404	3	−	−	PROPN
ma-136	404	4	1)α	1)α	NUM
ma-136	404	5	≥	≥	NOUN
ma-136	404	6	0	0	NUM
ma-136	404	7	(	(	PUNCT
ma-136	404	8	3.16	3.16	NUM
ma-136	404	9	)	)	PUNCT
ma-136	404	10	as	as	ADP
ma-136	404	11	|z	|z	PROPN
ma-136	404	12	|	|	PROPN
ma-136	404	13	→	→	SYM
ma-136	404	14	1−	1−	NUM
ma-136	404	15	for	for	ADP
ma-136	404	16	z	z	PROPN
ma-136	404	17	∈	∈	PROPN
ma-136	404	18	h.	h.	PROPN
ma-136	404	19	by	by	ADP
ma-136	404	20	(	(	PUNCT
ma-136	404	21	1.9	1.9	NUM
ma-136	404	22	)	)	PUNCT
ma-136	404	23	and	and	CCONJ
ma-136	404	24	(	(	PUNCT
ma-136	404	25	3.16	3.16	NUM
ma-136	404	26	)	)	PUNCT
ma-136	404	27	,	,	PUNCT
ma-136	404	28	we	we	PRON
ma-136	404	29	obtain	obtain	VERB
ma-136	404	30	t	t	NOUN
ma-136	404	31	(	(	PUNCT
ma-136	404	32	r	r	NOUN
ma-136	404	33	,	,	PUNCT
ma-136	404	34	a0	a0	PROPN
ma-136	404	35	)	)	PUNCT
ma-136	404	36	>	>	X
ma-136	405	1	γ	γ	X
ma-136	405	2	(	(	PUNCT
ma-136	405	3	1	1	NUM
ma-136	405	4	1−	1−	NUM
ma-136	405	5	|z	|z	PROPN
ma-136	405	6	|	|	ADV
ma-136	405	7	)	)	PUNCT
ma-136	405	8	µ	µ	X
ma-136	405	9	>	>	X
ma-136	405	10	(	(	PUNCT
ma-136	405	11	k	k	PROPN
ma-136	405	12	−	−	PROPN
ma-136	405	13	1)α	1)α	NUM
ma-136	405	14	(	(	PUNCT
ma-136	405	15	1	1	NUM
ma-136	405	16	1−	1−	NUM
ma-136	405	17	|z	|z	PROPN
ma-136	405	18	|	|	ADV
ma-136	405	19	)	)	PUNCT
ma-136	405	20	µ	µ	X
ma-136	405	21	≥	≥	NOUN
ma-136	405	22	α	α	PROPN
ma-136	405	23	(	(	PUNCT
ma-136	405	24	1	1	NUM
ma-136	405	25	1−	1−	NUM
ma-136	405	26	|z	|z	PROPN
ma-136	405	27	|	|	ADV
ma-136	405	28	)	)	PUNCT
ma-136	405	29	µ	µ	X
ma-136	405	30	≥	≥	NOUN
ma-136	405	31	t	t	PROPN
ma-136	405	32	(	(	PUNCT
ma-136	405	33	r	r	NOUN
ma-136	405	34	,	,	PUNCT
ma-136	405	35	ai	ai	NOUN
ma-136	405	36	)	)	PUNCT
ma-136	405	37	,	,	PUNCT
ma-136	405	38	(	(	PUNCT
ma-136	405	39	i	i	NOUN
ma-136	405	40	=	=	NOUN
ma-136	405	41	1	1	NUM
ma-136	405	42	,	,	PUNCT
ma-136	405	43	2	2	NUM
ma-136	405	44	,	,	PUNCT
ma-136	405	45	...	...	PUNCT
ma-136	405	46	,	,	PUNCT
ma-136	405	47	k	k	PROPN
ma-136	405	48	−	−	PROPN
ma-136	405	49	1	1	NUM
ma-136	405	50	)	)	PUNCT
ma-136	405	51	(	(	PUNCT
ma-136	405	52	3.17	3.17	NUM
ma-136	405	53	)	)	PUNCT
ma-136	405	54	as	as	ADP
ma-136	405	55	|z	|z	PROPN
ma-136	405	56	|	|	PROPN
ma-136	405	57	→	→	SYM
ma-136	405	58	1−	1−	NUM
ma-136	405	59	for	for	ADP
ma-136	405	60	z	z	PROPN
ma-136	405	61	∈	∈	PROPN
ma-136	405	62	h.	h.	NOUN
ma-136	405	63	by	by	ADP
ma-136	405	64	applying	apply	VERB
ma-136	405	65	lemma	lemma	PROPN
ma-136	405	66	2.2	2.2	NUM
ma-136	405	67	and	and	CCONJ
ma-136	405	68	substituting	substitute	VERB
ma-136	405	69	(	(	PUNCT
ma-136	405	70	3.17	3.17	NUM
ma-136	405	71	)	)	PUNCT
ma-136	405	72	into	into	ADP
ma-136	405	73	(	(	PUNCT
ma-136	405	74	3.10	3.10	NUM
ma-136	405	75	)	)	PUNCT
ma-136	405	76	,	,	PUNCT
ma-136	405	77	we	we	PRON
ma-136	405	78	get	get	VERB
ma-136	405	79	γ	γ	X
ma-136	405	80	(	(	PUNCT
ma-136	405	81	1	1	NUM
ma-136	405	82	1−	1−	NUM
ma-136	405	83	r	r	NOUN
ma-136	405	84	)	)	PUNCT
ma-136	405	85	µ	µ	NOUN
ma-136	405	86	≤	≤	NOUN
ma-136	405	87	(	(	PUNCT
ma-136	405	88	k	k	PROPN
ma-136	405	89	−	−	PROPN
ma-136	405	90	1)α	1)α	NUM
ma-136	405	91	(	(	PUNCT
ma-136	405	92	1	1	NUM
ma-136	405	93	1−	1−	NUM
ma-136	405	94	r	r	NOUN
ma-136	405	95	)	)	PUNCT
ma-136	405	96	µ	µ	PRON
ma-136	405	97	+	+	NOUN
ma-136	405	98	o	o	X
ma-136	405	99	(	(	PUNCT
ma-136	405	100	log+	log+	PROPN
ma-136	405	101	t	t	X
ma-136	405	102	(	(	PUNCT
ma-136	405	103	r	r	NOUN
ma-136	405	104	,	,	PUNCT
ma-136	405	105	f	f	PROPN
ma-136	405	106	)	)	PUNCT
ma-136	406	1	+	+	CCONJ
ma-136	406	2	log	log	NOUN
ma-136	406	3	(	(	PUNCT
ma-136	406	4	1	1	NUM
ma-136	406	5	1−	1−	NUM
ma-136	406	6	r	r	NOUN
ma-136	406	7	)	)	PUNCT
ma-136	406	8	)	)	PUNCT
ma-136	406	9	for	for	ADP
ma-136	406	10	all	all	DET
ma-136	406	11	z	z	NOUN
ma-136	406	12	satisfying	satisfy	VERB
ma-136	406	13	|z	|z	PROPN
ma-136	407	1	|	|	ADV
ma-136	407	2	=	=	SYM
ma-136	407	3	r	r	NOUN
ma-136	407	4	∈	∈	NOUN
ma-136	407	5	h1\e2	h1\e2	PUNCT
ma-136	407	6	as	as	ADP
ma-136	407	7	|z	|z	PROPN
ma-136	407	8	|	|	ADV
ma-136	407	9	=	=	SYM
ma-136	407	10	r	r	NOUN
ma-136	407	11	→	→	SYM
ma-136	407	12	1−.	1−.	NUM
ma-136	407	13	noting	note	VERB
ma-136	407	14	that	that	SCONJ
ma-136	407	15	γ	γ	PROPN
ma-136	407	16	>	>	X
ma-136	407	17	(	(	PUNCT
ma-136	407	18	k	k	PROPN
ma-136	407	19	−	−	PROPN
ma-136	407	20	1)α	1)α	NUM
ma-136	407	21	,	,	PUNCT
ma-136	407	22	by	by	ADP
ma-136	407	23	the	the	DET
ma-136	407	24	lastinequality	lastinequality	NOUN
ma-136	407	25	,	,	PUNCT
ma-136	407	26	we	we	PRON
ma-136	407	27	have	have	VERB
ma-136	407	28	(	(	PUNCT
ma-136	407	29	γ	γ	X
ma-136	407	30	−	−	PROPN
ma-136	407	31	(	(	PUNCT
ma-136	407	32	k	k	PROPN
ma-136	407	33	−	−	PROPN
ma-136	407	34	1)α	1)α	NUM
ma-136	407	35	)	)	PUNCT
ma-136	407	36	(	(	PUNCT
ma-136	407	37	1	1	NUM
ma-136	407	38	1−	1−	NUM
ma-136	407	39	r	r	NOUN
ma-136	407	40	)	)	PUNCT
ma-136	407	41	µ	µ	NOUN
ma-136	407	42	≤	≤	NOUN
ma-136	407	43	o	o	NOUN
ma-136	407	44	(	(	PUNCT
ma-136	407	45	log+	log+	PROPN
ma-136	407	46	t	t	X
ma-136	407	47	(	(	PUNCT
ma-136	407	48	r	r	NOUN
ma-136	407	49	,	,	PUNCT
ma-136	407	50	f	f	PROPN
ma-136	407	51	)	)	PUNCT
ma-136	408	1	+	+	CCONJ
ma-136	408	2	log	log	NOUN
ma-136	408	3	(	(	PUNCT
ma-136	408	4	1	1	NUM
ma-136	408	5	1−	1−	NUM
ma-136	408	6	r	r	NOUN
ma-136	408	7	)	)	PUNCT
ma-136	408	8	)	)	PUNCT
ma-136	408	9	(	(	PUNCT
ma-136	408	10	3.18	3.18	NUM
ma-136	408	11	)	)	PUNCT
ma-136	408	12	for	for	ADP
ma-136	408	13	all	all	PRON
ma-136	408	14	z	z	NOUN
ma-136	408	15	satisfying	satisfy	VERB
ma-136	408	16	|z	|z	PROPN
ma-136	409	1	|	|	ADV
ma-136	409	2	=	=	SYM
ma-136	409	3	r	r	NOUN
ma-136	409	4	∈	∈	NOUN
ma-136	409	5	h1\e2	h1\e2	PUNCT
ma-136	409	6	as	as	ADP
ma-136	409	7	|z	|z	PROPN
ma-136	409	8	|	|	ADV
ma-136	409	9	=	=	SYM
ma-136	409	10	r	r	NOUN
ma-136	409	11	→	→	SYM
ma-136	409	12	1−.	1−.	PROPN
ma-136	409	13	therefore	therefore	ADV
ma-136	409	14	,	,	PUNCT
ma-136	409	15	from	from	ADP
ma-136	409	16	(	(	PUNCT
ma-136	409	17	3.18	3.18	NUM
ma-136	409	18	)	)	PUNCT
ma-136	409	19	we	we	PRON
ma-136	409	20	obtain	obtain	VERB
ma-136	409	21	σ	σ	PROPN
ma-136	409	22	(	(	PUNCT
ma-136	409	23	f	f	PROPN
ma-136	409	24	)	)	PUNCT
ma-136	410	1	=	=	SYM
ma-136	410	2	σm	σm	X
ma-136	410	3	(	(	PUNCT
ma-136	410	4	f	f	NOUN
ma-136	410	5	)	)	PUNCT
ma-136	411	1	=	=	NOUN
ma-136	411	2	∞	∞	PROPN
ma-136	411	3	and	and	CCONJ
ma-136	411	4	σ2	σ2	PROPN
ma-136	411	5	(	(	PUNCT
ma-136	411	6	f	f	PROPN
ma-136	411	7	)	)	PUNCT
ma-136	412	1	=	=	SYM
ma-136	412	2	σm,2	σm,2	PROPN
ma-136	412	3	(	(	PUNCT
ma-136	412	4	f	f	PROPN
ma-136	412	5	)	)	PUNCT
ma-136	412	6	≥	≥	PROPN
ma-136	412	7	µ.	µ.	NOUN
ma-136	412	8	(	(	PUNCT
ma-136	412	9	3.19	3.19	NUM
ma-136	412	10	)	)	PUNCT
ma-136	412	11	https://doi.org/10.28924/ada/ma.3.10	https://doi.org/10.28924/ada/ma.3.10	ADV
ma-136	412	12	eur	eur	PROPN
ma-136	412	13	.	.	PUNCT
ma-136	413	1	j.	j.	PROPN
ma-136	413	2	math	math	PROPN
ma-136	413	3	.	.	PUNCT
ma-136	414	1	anal	anal	PROPN
ma-136	414	2	.	.	PUNCT
ma-136	415	1	10.28924	10.28924	NUM
ma-136	415	2	/	/	SYM
ma-136	415	3	ada	ada	NOUN
ma-136	415	4	/	/	SYM
ma-136	415	5	ma.3.10	ma.3.10	ADJ
ma-136	415	6	16by	16by	ADJ
ma-136	415	7	lemma	lemma	PROPN
ma-136	415	8	2.4	2.4	NUM
ma-136	415	9	,	,	PUNCT
ma-136	415	10	we	we	PRON
ma-136	415	11	get	get	VERB
ma-136	415	12	σ2	σ2	PROPN
ma-136	415	13	(	(	PUNCT
ma-136	415	14	f	f	PROPN
ma-136	415	15	)	)	PUNCT
ma-136	416	1	=	=	SYM
ma-136	416	2	σm,2	σm,2	PROPN
ma-136	416	3	(	(	PUNCT
ma-136	416	4	f	f	PROPN
ma-136	416	5	)	)	PUNCT
ma-136	416	6	≤	≤	PROPN
ma-136	416	7	max	max	PROPN
ma-136	416	8	{	{	PUNCT
ma-136	416	9	σm	σm	X
ma-136	416	10	(	(	PUNCT
ma-136	416	11	ai	ai	PROPN
ma-136	416	12	)	)	PUNCT
ma-136	416	13	:	:	PUNCT
ma-136	416	14	i	i	NOUN
ma-136	416	15	=	=	NOUN
ma-136	416	16	0	0	NUM
ma-136	416	17	,	,	PUNCT
ma-136	416	18	1	1	NUM
ma-136	416	19	,	,	PUNCT
ma-136	416	20	...	...	PUNCT
ma-136	416	21	,	,	PUNCT
ma-136	416	22	k	k	PROPN
ma-136	417	1	−	−	PROPN
ma-136	417	2	1	1	NUM
ma-136	417	3	}	}	PUNCT
ma-136	417	4	=	=	NOUN
ma-136	417	5	σm	σm	X
ma-136	417	6	(	(	PUNCT
ma-136	417	7	a0	a0	PROPN
ma-136	417	8	)	)	PUNCT
ma-136	417	9	=	=	SYM
ma-136	417	10	µ.	µ.	NOUN
ma-136	417	11	(	(	PUNCT
ma-136	417	12	3.20	3.20	NUM
ma-136	417	13	)	)	PUNCT
ma-136	417	14	therefore	therefore	ADV
ma-136	417	15	,	,	PUNCT
ma-136	417	16	by	by	ADP
ma-136	417	17	(	(	PUNCT
ma-136	417	18	3.19	3.19	NUM
ma-136	417	19	)	)	PUNCT
ma-136	417	20	and	and	CCONJ
ma-136	417	21	(	(	PUNCT
ma-136	417	22	3.20	3.20	NUM
ma-136	417	23	)	)	PUNCT
ma-136	417	24	,	,	PUNCT
ma-136	417	25	we	we	PRON
ma-136	417	26	obtain	obtain	VERB
ma-136	417	27	σ	σ	PROPN
ma-136	417	28	(	(	PUNCT
ma-136	417	29	f	f	PROPN
ma-136	417	30	)	)	PUNCT
ma-136	418	1	=	=	SYM
ma-136	418	2	σm	σm	X
ma-136	418	3	(	(	PUNCT
ma-136	418	4	f	f	NOUN
ma-136	418	5	)	)	PUNCT
ma-136	419	1	=	=	NOUN
ma-136	419	2	∞	∞	PROPN
ma-136	419	3	and	and	CCONJ
ma-136	419	4	σ2	σ2	PROPN
ma-136	419	5	(	(	PUNCT
ma-136	419	6	f	f	PROPN
ma-136	419	7	)	)	PUNCT
ma-136	420	1	=	=	SYM
ma-136	420	2	σm,2	σm,2	PROPN
ma-136	420	3	(	(	PUNCT
ma-136	420	4	f	f	X
ma-136	420	5	)	)	PUNCT
ma-136	420	6	=	=	PUNCT
ma-136	420	7	µ.	µ.	NOUN
ma-136	420	8	proof	proof	NOUN
ma-136	420	9	of	of	ADP
ma-136	420	10	theorem	theorem	ADJ
ma-136	420	11	1.4	1.4	NUM
ma-136	420	12	.	.	PUNCT
ma-136	421	1	if	if	SCONJ
ma-136	421	2	p	p	PROPN
ma-136	421	3	≥	≥	PUNCT
ma-136	421	4	q	q	X
ma-136	421	5	≥	≥	NUM
ma-136	421	6	2	2	NUM
ma-136	421	7	,	,	PUNCT
ma-136	421	8	we	we	PRON
ma-136	421	9	set	set	VERB
ma-136	421	10	α0	α0	PROPN
ma-136	421	11	=	=	SYM
ma-136	421	12	lim	lim	PROPN
ma-136	421	13	inf	inf	PROPN
ma-136	421	14	|z	|z	PROPN
ma-136	421	15	|→1−,z∈h	|→1−,z∈h	PROPN
ma-136	421	16	logp−1	logp−1	PROPN
ma-136	421	17	t	t	PROPN
ma-136	421	18	(	(	PUNCT
ma-136	421	19	r	r	PROPN
ma-136	421	20	,	,	PUNCT
ma-136	421	21	a0	a0	NOUN
ma-136	421	22	)	)	PUNCT
ma-136	421	23	(	(	PUNCT
ma-136	421	24	logq−1	logq−1	X
ma-136	421	25	(	(	PUNCT
ma-136	421	26	1	1	NUM
ma-136	421	27	1−|z	1−|z	NUM
ma-136	421	28	|	|	NOUN
ma-136	421	29	)	)	PUNCT
ma-136	421	30	)	)	PUNCT
ma-136	421	31	µ	µ	X
ma-136	421	32	,	,	PUNCT
ma-136	421	33	αi	αi	VERB
ma-136	421	34	=	=	SYM
ma-136	421	35	lim	lim	PROPN
ma-136	421	36	sup	sup	PROPN
ma-136	421	37	|z	|z	PROPN
ma-136	421	38	|→1−,z∈h	|→1−,z∈h	PROPN
ma-136	421	39	logp−1	logp−1	PROPN
ma-136	421	40	t	t	PROPN
ma-136	421	41	(	(	PUNCT
ma-136	421	42	r	r	NOUN
ma-136	421	43	,	,	PUNCT
ma-136	421	44	ai	ai	NOUN
ma-136	421	45	)	)	PUNCT
ma-136	421	46	(	(	PUNCT
ma-136	421	47	logq−1	logq−1	X
ma-136	421	48	(	(	PUNCT
ma-136	421	49	1	1	NUM
ma-136	421	50	1−|z	1−|z	NUM
ma-136	421	51	|	|	NOUN
ma-136	421	52	)	)	PUNCT
ma-136	421	53	)	)	PUNCT
ma-136	421	54	µ	µ	X
ma-136	421	55	,	,	PUNCT
ma-136	421	56	(	(	PUNCT
ma-136	421	57	i	i	NOUN
ma-136	421	58	=	=	NOUN
ma-136	421	59	1	1	NUM
ma-136	421	60	,	,	PUNCT
ma-136	421	61	2	2	NUM
ma-136	421	62	,	,	PUNCT
ma-136	421	63	...	...	PUNCT
ma-136	421	64	,	,	PUNCT
ma-136	421	65	k	k	PROPN
ma-136	421	66	−	−	PROPN
ma-136	421	67	1	1	NUM
ma-136	421	68	)	)	PUNCT
ma-136	421	69	.	.	PUNCT
ma-136	422	1	by	by	ADP
ma-136	422	2	(	(	PUNCT
ma-136	422	3	1.10	1.10	NUM
ma-136	422	4	)	)	PUNCT
ma-136	422	5	,	,	PUNCT
ma-136	422	6	there	there	PRON
ma-136	422	7	exist	exist	VERB
ma-136	422	8	real	real	ADJ
ma-136	422	9	numbers	number	NOUN
ma-136	422	10	α	α	PRON
ma-136	422	11	,	,	PUNCT
ma-136	422	12	γ	γ	PROPN
ma-136	422	13	such	such	ADJ
ma-136	422	14	that	that	SCONJ
ma-136	422	15	αi	αi	VERB
ma-136	422	16	<	<	X
ma-136	422	17	α	α	X
ma-136	422	18	<	<	X
ma-136	422	19	γ	γ	X
ma-136	422	20	<	<	X
ma-136	422	21	α0	α0	PROPN
ma-136	422	22	,	,	PUNCT
ma-136	422	23	i	i	NOUN
ma-136	422	24	=	=	NOUN
ma-136	422	25	1	1	NUM
ma-136	422	26	,	,	PUNCT
ma-136	422	27	2	2	NUM
ma-136	422	28	,	,	PUNCT
ma-136	422	29	...	...	PUNCT
ma-136	422	30	,	,	PUNCT
ma-136	423	1	k	k	PROPN
ma-136	423	2	−	−	PROPN
ma-136	424	1	1	1	X
ma-136	424	2	.	.	PUNCT
ma-136	424	3	it	it	PRON
ma-136	424	4	yields	yield	VERB
ma-136	424	5	logp−1	logp−1	PROPN
ma-136	424	6	t	t	PROPN
ma-136	424	7	(	(	PUNCT
ma-136	424	8	r	r	NOUN
ma-136	424	9	,	,	PUNCT
ma-136	424	10	ai	ai	NOUN
ma-136	424	11	)	)	PUNCT
ma-136	424	12	(	(	PUNCT
ma-136	424	13	logq−1	logq−1	X
ma-136	424	14	(	(	PUNCT
ma-136	424	15	1	1	NUM
ma-136	424	16	1−|z	1−|z	NUM
ma-136	424	17	|	|	NOUN
ma-136	424	18	)	)	PUNCT
ma-136	424	19	)	)	PUNCT
ma-136	424	20	µ	µ	X
ma-136	424	21	<	<	X
ma-136	424	22	α	α	X
ma-136	424	23	<	<	X
ma-136	424	24	γ	γ	X
ma-136	424	25	<	<	X
ma-136	424	26	logp−1	logp−1	PROPN
ma-136	424	27	t	t	PROPN
ma-136	424	28	(	(	PUNCT
ma-136	424	29	r	r	PROPN
ma-136	424	30	,	,	PUNCT
ma-136	424	31	a0	a0	NOUN
ma-136	424	32	)	)	PUNCT
ma-136	424	33	(	(	PUNCT
ma-136	424	34	logq−1	logq−1	X
ma-136	424	35	(	(	PUNCT
ma-136	424	36	1	1	NUM
ma-136	424	37	1−|z	1−|z	NUM
ma-136	424	38	|	|	NOUN
ma-136	424	39	)	)	PUNCT
ma-136	424	40	)	)	PUNCT
ma-136	424	41	µ	µ	X
ma-136	424	42	as	as	ADP
ma-136	424	43	|z	|z	PROPN
ma-136	424	44	|	|	PROPN
ma-136	424	45	→	→	SYM
ma-136	424	46	1−	1−	NUM
ma-136	424	47	for	for	ADP
ma-136	424	48	z	z	PROPN
ma-136	424	49	∈	∈	PROPN
ma-136	424	50	h.	h.	PROPN
ma-136	424	51	hence	hence	ADV
ma-136	424	52	,	,	PUNCT
ma-136	424	53	we	we	PRON
ma-136	424	54	have	have	VERB
ma-136	424	55	t	t	NOUN
ma-136	424	56	(	(	PUNCT
ma-136	424	57	r	r	NOUN
ma-136	424	58	,	,	PUNCT
ma-136	424	59	a0	a0	NOUN
ma-136	424	60	)	)	PUNCT
ma-136	424	61	>	>	X
ma-136	425	1	expp−1	expp−1	NOUN
ma-136	425	2	{	{	PUNCT
ma-136	425	3	γ	γ	X
ma-136	425	4	(	(	PUNCT
ma-136	425	5	logq−1	logq−1	X
ma-136	425	6	(	(	PUNCT
ma-136	425	7	1	1	NUM
ma-136	425	8	1−	1−	NUM
ma-136	425	9	|z	|z	NOUN
ma-136	425	10	|	|	ADV
ma-136	425	11	)	)	PUNCT
ma-136	425	12	)	)	PUNCT
ma-136	425	13	µ	µ	X
ma-136	425	14	}	}	PUNCT
ma-136	425	15	>	>	X
ma-136	425	16	expp−1	expp−1	NOUN
ma-136	425	17	{	{	PUNCT
ma-136	425	18	α	α	PROPN
ma-136	425	19	(	(	PUNCT
ma-136	425	20	logq−1	logq−1	X
ma-136	425	21	(	(	PUNCT
ma-136	425	22	1	1	NUM
ma-136	425	23	1−	1−	NUM
ma-136	425	24	|z	|z	NOUN
ma-136	425	25	|	|	ADV
ma-136	425	26	)	)	PUNCT
ma-136	425	27	)	)	PUNCT
ma-136	425	28	µ	µ	X
ma-136	425	29	}	}	PUNCT
ma-136	425	30	≥	≥	NOUN
ma-136	425	31	t	t	NOUN
ma-136	425	32	(	(	PUNCT
ma-136	425	33	r	r	NOUN
ma-136	425	34	,	,	PUNCT
ma-136	425	35	ai	ai	NOUN
ma-136	425	36	)	)	PUNCT
ma-136	425	37	,	,	PUNCT
ma-136	425	38	(	(	PUNCT
ma-136	425	39	i	i	NOUN
ma-136	425	40	=	=	NOUN
ma-136	425	41	1	1	NUM
ma-136	425	42	,	,	PUNCT
ma-136	425	43	2	2	NUM
ma-136	425	44	,	,	PUNCT
ma-136	425	45	...	...	PUNCT
ma-136	425	46	,	,	PUNCT
ma-136	425	47	k	k	PROPN
ma-136	426	1	−	−	PROPN
ma-136	426	2	1	1	NUM
ma-136	426	3	)	)	PUNCT
ma-136	426	4	as	as	ADP
ma-136	426	5	|z	|z	PROPN
ma-136	426	6	|	|	PROPN
ma-136	426	7	→	→	SYM
ma-136	426	8	1−	1−	NUM
ma-136	426	9	for	for	ADP
ma-136	426	10	z	z	PROPN
ma-136	426	11	∈	∈	PROPN
ma-136	426	12	h.	h.	NOUN
ma-136	426	13	then	then	ADV
ma-136	426	14	,	,	PUNCT
ma-136	426	15	by	by	ADP
ma-136	426	16	using	use	VERB
ma-136	426	17	the	the	DET
ma-136	426	18	same	same	ADJ
ma-136	426	19	proof	proof	NOUN
ma-136	426	20	of	of	ADP
ma-136	426	21	theorem	theorem	NOUN
ma-136	426	22	1.3	1.3	NUM
ma-136	426	23	,	,	PUNCT
ma-136	426	24	we	we	PRON
ma-136	426	25	get	get	VERB
ma-136	426	26	σ[p	σ[p	NOUN
ma-136	426	27	,	,	PUNCT
ma-136	426	28	q	q	X
ma-136	426	29	]	]	X
ma-136	426	30	(	(	PUNCT
ma-136	426	31	f	f	X
ma-136	426	32	)	)	PUNCT
ma-136	426	33	=	=	SYM
ma-136	426	34	σm,[p	σm,[p	NOUN
ma-136	426	35	,	,	PUNCT
ma-136	426	36	q	q	X
ma-136	426	37	]	]	X
ma-136	426	38	(	(	PUNCT
ma-136	426	39	f	f	X
ma-136	426	40	)	)	PUNCT
ma-136	427	1	=	=	NOUN
ma-136	427	2	∞	∞	NOUN
ma-136	427	3	and	and	CCONJ
ma-136	427	4	σ[p+1,q	σ[p+1,q	NOUN
ma-136	427	5	]	]	PUNCT
ma-136	427	6	(	(	PUNCT
ma-136	427	7	f	f	X
ma-136	427	8	)	)	PUNCT
ma-136	427	9	=	=	SYM
ma-136	428	1	σm,[p+1,q	σm,[p+1,q	X
ma-136	428	2	]	]	PUNCT
ma-136	428	3	(	(	PUNCT
ma-136	428	4	f	f	PROPN
ma-136	428	5	)	)	PUNCT
ma-136	428	6	≥	≥	PROPN
ma-136	428	7	µ	µ	NOUN
ma-136	428	8	,	,	PUNCT
ma-136	428	9	and	and	CCONJ
ma-136	428	10	by	by	ADP
ma-136	428	11	lemma	lemma	PROPN
ma-136	428	12	2.4	2.4	NUM
ma-136	428	13	we	we	PRON
ma-136	428	14	obtain	obtain	VERB
ma-136	428	15	the	the	DET
ma-136	428	16	conclusion	conclusion	NOUN
ma-136	428	17	of	of	ADP
ma-136	428	18	theorem	theorem	ADJ
ma-136	428	19	1.4.if	1.4.if	PROPN
ma-136	428	20	p	p	NOUN
ma-136	428	21	=	=	X
ma-136	428	22	q	q	NOUN
ma-136	429	1	=	=	NOUN
ma-136	429	2	1	1	NUM
ma-136	429	3	,	,	PUNCT
ma-136	429	4	we	we	PRON
ma-136	429	5	set	set	VERB
ma-136	429	6	α0	α0	PROPN
ma-136	429	7	=	=	SYM
ma-136	429	8	lim	lim	PROPN
ma-136	429	9	inf	inf	PROPN
ma-136	429	10	|z	|z	PROPN
ma-136	429	11	|→1−,z∈h	|→1−,z∈h	PROPN
ma-136	429	12	t	t	PROPN
ma-136	429	13	(	(	PUNCT
ma-136	429	14	r	r	PROPN
ma-136	429	15	,	,	PUNCT
ma-136	429	16	a0	a0	NOUN
ma-136	429	17	)	)	PUNCT
ma-136	429	18	(	(	PUNCT
ma-136	429	19	1	1	NUM
ma-136	429	20	1−|z	1−|z	NUM
ma-136	429	21	|	|	ADJ
ma-136	429	22	)	)	PUNCT
ma-136	429	23	µ	µ	NOUN
ma-136	429	24	,	,	PUNCT
ma-136	429	25	αi	αi	VERB
ma-136	429	26	=	=	SYM
ma-136	429	27	lim	lim	PROPN
ma-136	429	28	sup	sup	PROPN
ma-136	429	29	|z	|z	PROPN
ma-136	429	30	|→1−,z∈h	|→1−,z∈h	PROPN
ma-136	429	31	(	(	PUNCT
ma-136	429	32	k	k	PROPN
ma-136	429	33	−	−	PROPN
ma-136	429	34	1)t	1)t	PROPN
ma-136	429	35	(	(	PUNCT
ma-136	429	36	r	r	NOUN
ma-136	429	37	,	,	PUNCT
ma-136	429	38	ai	ai	NOUN
ma-136	429	39	)	)	PUNCT
ma-136	429	40	(	(	PUNCT
ma-136	429	41	1	1	NUM
ma-136	429	42	1−|z	1−|z	NUM
ma-136	429	43	|	|	ADJ
ma-136	429	44	)	)	PUNCT
ma-136	429	45	µ	µ	NOUN
ma-136	429	46	,	,	PUNCT
ma-136	429	47	(	(	PUNCT
ma-136	429	48	i	i	NOUN
ma-136	429	49	=	=	NOUN
ma-136	429	50	1	1	NUM
ma-136	429	51	,	,	PUNCT
ma-136	429	52	2	2	NUM
ma-136	429	53	,	,	PUNCT
ma-136	429	54	...	...	PUNCT
ma-136	429	55	,	,	PUNCT
ma-136	429	56	k	k	PROPN
ma-136	430	1	−	−	PROPN
ma-136	430	2	1	1	NUM
ma-136	430	3	)	)	PUNCT
ma-136	430	4	.	.	PUNCT
ma-136	431	1	by	by	ADP
ma-136	431	2	(	(	PUNCT
ma-136	431	3	1.11	1.11	NUM
ma-136	431	4	)	)	PUNCT
ma-136	431	5	,	,	PUNCT
ma-136	431	6	there	there	PRON
ma-136	431	7	exist	exist	VERB
ma-136	431	8	real	real	ADJ
ma-136	431	9	numbers	number	NOUN
ma-136	431	10	α	α	PRON
ma-136	431	11	,	,	PUNCT
ma-136	431	12	γ	γ	PROPN
ma-136	431	13	such	such	ADJ
ma-136	431	14	that	that	SCONJ
ma-136	431	15	αi	αi	VERB
ma-136	431	16	<	<	X
ma-136	431	17	α	α	X
ma-136	431	18	<	<	X
ma-136	431	19	γ	γ	X
ma-136	431	20	<	<	X
ma-136	431	21	α0	α0	PROPN
ma-136	431	22	,	,	PUNCT
ma-136	431	23	i	i	NOUN
ma-136	431	24	=	=	NOUN
ma-136	431	25	1	1	NUM
ma-136	431	26	,	,	PUNCT
ma-136	431	27	2	2	NUM
ma-136	431	28	,	,	PUNCT
ma-136	431	29	...	...	PUNCT
ma-136	431	30	,	,	PUNCT
ma-136	432	1	k	k	PROPN
ma-136	432	2	−	−	PROPN
ma-136	433	1	1	1	X
ma-136	433	2	.	.	PUNCT
ma-136	434	1	it	it	PRON
ma-136	434	2	yields	yield	VERB
ma-136	434	3	(	(	PUNCT
ma-136	434	4	k	k	PROPN
ma-136	434	5	−	−	PROPN
ma-136	434	6	1)t	1)t	PROPN
ma-136	434	7	(	(	PUNCT
ma-136	434	8	r	r	NOUN
ma-136	434	9	,	,	PUNCT
ma-136	434	10	ai	ai	NOUN
ma-136	434	11	)	)	PUNCT
ma-136	434	12	(	(	PUNCT
ma-136	434	13	1	1	NUM
ma-136	434	14	1−|z	1−|z	NUM
ma-136	434	15	|	|	NOUN
ma-136	434	16	)	)	PUNCT
ma-136	434	17	µ	µ	X
ma-136	434	18	<	<	X
ma-136	434	19	α	α	X
ma-136	434	20	<	<	X
ma-136	434	21	γ	γ	X
ma-136	434	22	<	<	X
ma-136	434	23	t	t	PROPN
ma-136	434	24	(	(	PUNCT
ma-136	434	25	r	r	PROPN
ma-136	434	26	,	,	PUNCT
ma-136	434	27	a0	a0	NOUN
ma-136	434	28	)	)	PUNCT
ma-136	434	29	(	(	PUNCT
ma-136	434	30	1	1	NUM
ma-136	434	31	1−|z	1−|z	NUM
ma-136	434	32	|	|	NOUN
ma-136	434	33	)	)	PUNCT
ma-136	434	34	µ	µ	X
ma-136	434	35	(	(	PUNCT
ma-136	434	36	3.21	3.21	NUM
ma-136	434	37	)	)	PUNCT
ma-136	434	38	as	as	ADP
ma-136	434	39	|z	|z	PROPN
ma-136	434	40	|	|	PROPN
ma-136	434	41	→	→	SYM
ma-136	434	42	1−	1−	NUM
ma-136	434	43	for	for	ADP
ma-136	434	44	z	z	PROPN
ma-136	434	45	∈	∈	PROPN
ma-136	434	46	h.	h.	PROPN
ma-136	434	47	by	by	ADP
ma-136	434	48	(	(	PUNCT
ma-136	434	49	3.21	3.21	NUM
ma-136	434	50	)	)	PUNCT
ma-136	434	51	,	,	PUNCT
ma-136	434	52	we	we	PRON
ma-136	434	53	obtain	obtain	VERB
ma-136	434	54	t	t	NOUN
ma-136	434	55	(	(	PUNCT
ma-136	434	56	r	r	NOUN
ma-136	434	57	,	,	PUNCT
ma-136	434	58	a0	a0	PROPN
ma-136	434	59	)	)	PUNCT
ma-136	434	60	>	>	X
ma-136	434	61	γ	γ	X
ma-136	434	62	(	(	PUNCT
ma-136	434	63	1	1	NUM
ma-136	434	64	1−	1−	NUM
ma-136	434	65	|z	|z	PROPN
ma-136	434	66	|	|	ADV
ma-136	434	67	)	)	PUNCT
ma-136	434	68	µ	µ	X
ma-136	434	69	>	>	X
ma-136	434	70	α	α	PROPN
ma-136	434	71	(	(	PUNCT
ma-136	434	72	1	1	NUM
ma-136	434	73	1−	1−	NUM
ma-136	434	74	|z	|z	PROPN
ma-136	434	75	|	|	ADV
ma-136	434	76	)	)	PUNCT
ma-136	434	77	µ	µ	NOUN
ma-136	434	78	≥	≥	X
ma-136	434	79	(	(	PUNCT
ma-136	434	80	k	k	PROPN
ma-136	434	81	−	−	PROPN
ma-136	434	82	1)t	1)t	PROPN
ma-136	434	83	(	(	PUNCT
ma-136	434	84	r	r	NOUN
ma-136	434	85	,	,	PUNCT
ma-136	434	86	ai	ai	NOUN
ma-136	434	87	)	)	PUNCT
ma-136	434	88	,	,	PUNCT
ma-136	434	89	(	(	PUNCT
ma-136	434	90	i	i	NOUN
ma-136	434	91	=	=	NOUN
ma-136	434	92	1	1	NUM
ma-136	434	93	,	,	PUNCT
ma-136	434	94	2	2	NUM
ma-136	434	95	,	,	PUNCT
ma-136	434	96	...	...	PUNCT
ma-136	434	97	,	,	PUNCT
ma-136	434	98	k	k	PROPN
ma-136	435	1	−	−	PROPN
ma-136	435	2	1	1	NUM
ma-136	435	3	)	)	PUNCT
ma-136	435	4	(	(	PUNCT
ma-136	435	5	3.22	3.22	NUM
ma-136	435	6	)	)	PUNCT
ma-136	435	7	https://doi.org/10.28924/ada/ma.3.10	https://doi.org/10.28924/ada/ma.3.10	ADV
ma-136	435	8	eur	eur	PROPN
ma-136	435	9	.	.	PUNCT
ma-136	436	1	j.	j.	PROPN
ma-136	436	2	math	math	PROPN
ma-136	436	3	.	.	PUNCT
ma-136	437	1	anal	anal	PROPN
ma-136	437	2	.	.	PUNCT
ma-136	438	1	10.28924	10.28924	NUM
ma-136	438	2	/	/	SYM
ma-136	438	3	ada	ada	NOUN
ma-136	438	4	/	/	PROPN
ma-136	438	5	ma.3.10	ma.3.10	NOUN
ma-136	439	1	17as	17as	PROPN
ma-136	439	2	|z	|z	PROPN
ma-136	440	1	|	|	PROPN
ma-136	440	2	→	→	SYM
ma-136	440	3	1−	1−	NUM
ma-136	440	4	for	for	ADP
ma-136	440	5	z	z	PROPN
ma-136	440	6	∈	∈	PROPN
ma-136	440	7	h.	h.	NOUN
ma-136	440	8	by	by	ADP
ma-136	440	9	applying	apply	VERB
ma-136	440	10	lemma	lemma	PROPN
ma-136	440	11	2.2	2.2	NUM
ma-136	440	12	and	and	CCONJ
ma-136	440	13	substituting	substitute	VERB
ma-136	440	14	(	(	PUNCT
ma-136	440	15	3.22	3.22	NUM
ma-136	440	16	)	)	PUNCT
ma-136	440	17	into	into	ADP
ma-136	440	18	(	(	PUNCT
ma-136	440	19	3.10	3.10	NUM
ma-136	440	20	)	)	PUNCT
ma-136	440	21	,	,	PUNCT
ma-136	440	22	we	we	PRON
ma-136	440	23	get	get	VERB
ma-136	440	24	γ	γ	X
ma-136	440	25	(	(	PUNCT
ma-136	440	26	1	1	NUM
ma-136	440	27	1−	1−	NUM
ma-136	440	28	r	r	NOUN
ma-136	440	29	)	)	PUNCT
ma-136	440	30	µ	µ	NOUN
ma-136	440	31	≤	≤	NOUN
ma-136	440	32	α	α	NOUN
ma-136	440	33	(	(	PUNCT
ma-136	440	34	1	1	NUM
ma-136	440	35	1−	1−	NUM
ma-136	440	36	r	r	NOUN
ma-136	440	37	)	)	PUNCT
ma-136	440	38	µ	µ	PRON
ma-136	441	1	+	+	NOUN
ma-136	441	2	o	o	X
ma-136	441	3	(	(	PUNCT
ma-136	441	4	log+	log+	PROPN
ma-136	441	5	t	t	X
ma-136	441	6	(	(	PUNCT
ma-136	441	7	r	r	NOUN
ma-136	441	8	,	,	PUNCT
ma-136	441	9	f	f	PROPN
ma-136	441	10	)	)	PUNCT
ma-136	442	1	+	+	CCONJ
ma-136	442	2	log	log	NOUN
ma-136	442	3	(	(	PUNCT
ma-136	442	4	1	1	NUM
ma-136	442	5	1−	1−	NUM
ma-136	442	6	r	r	NOUN
ma-136	442	7	)	)	PUNCT
ma-136	442	8	)	)	PUNCT
ma-136	442	9	for	for	ADP
ma-136	442	10	all	all	DET
ma-136	442	11	z	z	NOUN
ma-136	442	12	satisfying	satisfy	VERB
ma-136	442	13	|z	|z	PROPN
ma-136	443	1	|	|	ADV
ma-136	443	2	=	=	SYM
ma-136	443	3	r	r	NOUN
ma-136	443	4	∈	∈	NOUN
ma-136	443	5	h1\e2	h1\e2	PUNCT
ma-136	443	6	as	as	ADP
ma-136	443	7	|z	|z	PROPN
ma-136	443	8	|	|	ADV
ma-136	443	9	=	=	SYM
ma-136	443	10	r	r	NOUN
ma-136	443	11	→	→	SYM
ma-136	443	12	1−.	1−.	NUM
ma-136	443	13	noting	note	VERB
ma-136	443	14	that	that	SCONJ
ma-136	443	15	γ	γ	PROPN
ma-136	443	16	>	>	X
ma-136	443	17	α	α	PROPN
ma-136	443	18	,	,	PUNCT
ma-136	443	19	by	by	ADP
ma-136	443	20	the	the	DET
ma-136	443	21	last	last	ADJ
ma-136	443	22	inequality	inequality	NOUN
ma-136	443	23	,	,	PUNCT
ma-136	443	24	we	we	PRON
ma-136	443	25	have	have	VERB
ma-136	443	26	(	(	PUNCT
ma-136	443	27	γ	γ	X
ma-136	443	28	−	−	PROPN
ma-136	443	29	α	α	NOUN
ma-136	443	30	)	)	PUNCT
ma-136	443	31	(	(	PUNCT
ma-136	443	32	1	1	NUM
ma-136	443	33	1−	1−	NUM
ma-136	443	34	r	r	NOUN
ma-136	443	35	)	)	PUNCT
ma-136	444	1	µ	µ	NOUN
ma-136	444	2	≤	≤	NOUN
ma-136	445	1	o	o	NOUN
ma-136	446	1	(	(	PUNCT
ma-136	446	2	log+	log+	PROPN
ma-136	446	3	t	t	X
ma-136	446	4	(	(	PUNCT
ma-136	446	5	r	r	NOUN
ma-136	446	6	,	,	PUNCT
ma-136	446	7	f	f	PROPN
ma-136	446	8	)	)	PUNCT
ma-136	447	1	+	+	CCONJ
ma-136	447	2	log	log	NOUN
ma-136	447	3	(	(	PUNCT
ma-136	447	4	1	1	NUM
ma-136	447	5	1−	1−	NUM
ma-136	447	6	r	r	NOUN
ma-136	447	7	)	)	PUNCT
ma-136	447	8	)	)	PUNCT
ma-136	447	9	(	(	PUNCT
ma-136	447	10	3.23	3.23	NUM
ma-136	447	11	)	)	PUNCT
ma-136	447	12	for	for	ADP
ma-136	447	13	all	all	PRON
ma-136	447	14	z	z	NOUN
ma-136	447	15	satisfying	satisfy	VERB
ma-136	447	16	|z	|z	PROPN
ma-136	448	1	|	|	ADV
ma-136	448	2	=	=	SYM
ma-136	448	3	r	r	NOUN
ma-136	448	4	∈	∈	NOUN
ma-136	448	5	h1\e2	h1\e2	PUNCT
ma-136	448	6	as	as	ADP
ma-136	448	7	|z	|z	PROPN
ma-136	448	8	|	|	ADV
ma-136	448	9	=	=	SYM
ma-136	448	10	r	r	NOUN
ma-136	448	11	→	→	SYM
ma-136	448	12	1−.	1−.	PROPN
ma-136	448	13	therefore	therefore	ADV
ma-136	448	14	,	,	PUNCT
ma-136	448	15	from	from	ADP
ma-136	448	16	(	(	PUNCT
ma-136	448	17	3.23	3.23	NUM
ma-136	448	18	)	)	PUNCT
ma-136	448	19	we	we	PRON
ma-136	448	20	obtain	obtain	VERB
ma-136	448	21	σ	σ	PROPN
ma-136	448	22	(	(	PUNCT
ma-136	448	23	f	f	PROPN
ma-136	448	24	)	)	PUNCT
ma-136	448	25	=	=	SYM
ma-136	449	1	σm	σm	X
ma-136	449	2	(	(	PUNCT
ma-136	449	3	f	f	NOUN
ma-136	449	4	)	)	PUNCT
ma-136	450	1	=	=	NOUN
ma-136	450	2	∞	∞	PROPN
ma-136	450	3	and	and	CCONJ
ma-136	450	4	σ2	σ2	PROPN
ma-136	450	5	(	(	PUNCT
ma-136	450	6	f	f	PROPN
ma-136	450	7	)	)	PUNCT
ma-136	451	1	=	=	SYM
ma-136	451	2	σm,2	σm,2	PROPN
ma-136	451	3	(	(	PUNCT
ma-136	451	4	f	f	PROPN
ma-136	451	5	)	)	PUNCT
ma-136	451	6	≥	≥	PROPN
ma-136	451	7	µ.	µ.	NOUN
ma-136	451	8	(	(	PUNCT
ma-136	451	9	3.24	3.24	NUM
ma-136	451	10	)	)	PUNCT
ma-136	451	11	by	by	ADP
ma-136	451	12	lemma	lemma	PROPN
ma-136	451	13	2.4	2.4	NUM
ma-136	451	14	,	,	PUNCT
ma-136	451	15	we	we	PRON
ma-136	451	16	get	get	VERB
ma-136	451	17	σ2	σ2	PROPN
ma-136	451	18	(	(	PUNCT
ma-136	451	19	f	f	PROPN
ma-136	451	20	)	)	PUNCT
ma-136	452	1	=	=	SYM
ma-136	452	2	σm,2	σm,2	PROPN
ma-136	452	3	(	(	PUNCT
ma-136	452	4	f	f	PROPN
ma-136	452	5	)	)	PUNCT
ma-136	452	6	≤	≤	PROPN
ma-136	452	7	max	max	PROPN
ma-136	452	8	{	{	PUNCT
ma-136	452	9	σm	σm	X
ma-136	452	10	(	(	PUNCT
ma-136	452	11	ai	ai	PROPN
ma-136	452	12	)	)	PUNCT
ma-136	452	13	:	:	PUNCT
ma-136	452	14	i	i	NOUN
ma-136	452	15	=	=	NOUN
ma-136	452	16	0	0	NUM
ma-136	452	17	,	,	PUNCT
ma-136	452	18	1	1	NUM
ma-136	452	19	,	,	PUNCT
ma-136	452	20	...	...	PUNCT
ma-136	452	21	,	,	PUNCT
ma-136	452	22	k	k	PROPN
ma-136	453	1	−	−	PROPN
ma-136	453	2	1	1	NUM
ma-136	453	3	}	}	PUNCT
ma-136	453	4	=	=	NOUN
ma-136	453	5	σm	σm	X
ma-136	453	6	(	(	PUNCT
ma-136	453	7	a0	a0	PROPN
ma-136	453	8	)	)	PUNCT
ma-136	453	9	=	=	SYM
ma-136	453	10	µ.	µ.	NOUN
ma-136	453	11	(	(	PUNCT
ma-136	453	12	3.25	3.25	NUM
ma-136	453	13	)	)	PUNCT
ma-136	453	14	therefore	therefore	ADV
ma-136	453	15	,	,	PUNCT
ma-136	453	16	by	by	ADP
ma-136	453	17	(	(	PUNCT
ma-136	453	18	3.24	3.24	NUM
ma-136	453	19	)	)	PUNCT
ma-136	453	20	and	and	CCONJ
ma-136	453	21	(	(	PUNCT
ma-136	453	22	3.25	3.25	NUM
ma-136	453	23	)	)	PUNCT
ma-136	453	24	,	,	PUNCT
ma-136	453	25	we	we	PRON
ma-136	453	26	obtain	obtain	VERB
ma-136	453	27	σ	σ	PROPN
ma-136	453	28	(	(	PUNCT
ma-136	453	29	f	f	PROPN
ma-136	453	30	)	)	PUNCT
ma-136	454	1	=	=	SYM
ma-136	454	2	σm	σm	X
ma-136	454	3	(	(	PUNCT
ma-136	454	4	f	f	NOUN
ma-136	454	5	)	)	PUNCT
ma-136	455	1	=	=	NOUN
ma-136	455	2	∞	∞	PROPN
ma-136	455	3	and	and	CCONJ
ma-136	455	4	σ2	σ2	PROPN
ma-136	455	5	(	(	PUNCT
ma-136	455	6	f	f	PROPN
ma-136	455	7	)	)	PUNCT
ma-136	456	1	=	=	SYM
ma-136	456	2	σm,2	σm,2	PROPN
ma-136	456	3	(	(	PUNCT
ma-136	456	4	f	f	X
ma-136	456	5	)	)	PUNCT
ma-136	456	6	=	=	PUNCT
ma-136	456	7	µ.	µ.	NOUN
ma-136	456	8	proof	proof	NOUN
ma-136	456	9	of	of	ADP
ma-136	456	10	theorems	theorem	NOUN
ma-136	456	11	1.5	1.5	NUM
ma-136	456	12	and	and	CCONJ
ma-136	456	13	1.6	1.6	NUM
ma-136	456	14	.	.	PUNCT
ma-136	456	15	suppose	suppose	VERB
ma-136	456	16	that	that	SCONJ
ma-136	456	17	every	every	DET
ma-136	456	18	meromorphic	meromorphic	ADJ
ma-136	456	19	(	(	PUNCT
ma-136	456	20	or	or	CCONJ
ma-136	456	21	analytic	analytic	ADJ
ma-136	456	22	)	)	PUNCT
ma-136	456	23	solution	solution	NOUN
ma-136	456	24	f	f	PROPN
ma-136	456	25	ofequation	ofequation	NOUN
ma-136	456	26	(	(	PUNCT
ma-136	456	27	1.2	1.2	NUM
ma-136	456	28	)	)	PUNCT
ma-136	456	29	not	not	PART
ma-136	456	30	being	be	AUX
ma-136	456	31	identically	identically	ADV
ma-136	456	32	equal	equal	ADJ
ma-136	456	33	to	to	ADP
ma-136	456	34	0	0	NUM
ma-136	456	35	.	.	PUNCT
ma-136	456	36	from	from	ADP
ma-136	456	37	(	(	PUNCT
ma-136	456	38	1.2	1.2	NUM
ma-136	456	39	)	)	PUNCT
ma-136	456	40	,	,	PUNCT
ma-136	456	41	we	we	PRON
ma-136	456	42	get	get	VERB
ma-136	456	43	a0	a0	NOUN
ma-136	456	44	(	(	PUNCT
ma-136	456	45	z	z	NOUN
ma-136	456	46	)	)	PUNCT
ma-136	456	47	≤	≤	NUM
ma-136	456	48	|ak	|ak	X
ma-136	456	49	(	(	PUNCT
ma-136	456	50	z)|	z)|	ADP
ma-136	456	51	∣∣∣∣∣	∣∣∣∣∣	PROPN
ma-136	456	52	f	f	PROPN
ma-136	456	53	(	(	PUNCT
ma-136	456	54	k)f	k)f	PROPN
ma-136	456	55	∣∣∣∣∣+	∣∣∣∣∣+	PROPN
ma-136	456	56	|ak−1	|ak−1	NUM
ma-136	456	57	(	(	PUNCT
ma-136	456	58	z)|	z)|	X
ma-136	456	59	∣∣∣∣∣	∣∣∣∣∣	PROPN
ma-136	456	60	f	f	PROPN
ma-136	456	61	(	(	PUNCT
ma-136	456	62	k−1)f	k−1)f	PROPN
ma-136	456	63	∣∣∣∣∣+	∣∣∣∣∣+	PROPN
ma-136	456	64	·	·	PUNCT
ma-136	456	65	·	·	PUNCT
ma-136	456	66	·	·	PUNCT
ma-136	456	67	+	+	NUM
ma-136	456	68	|a1	|a1	NOUN
ma-136	456	69	(	(	PUNCT
ma-136	456	70	z)|	z)|	NOUN
ma-136	456	71	∣∣∣∣	∣∣∣∣	PROPN
ma-136	456	72	f	f	PROPN
ma-136	456	73	′f	′f	PROPN
ma-136	456	74	∣∣∣∣	∣∣∣∣	PROPN
ma-136	456	75	.	.	PUNCT
ma-136	456	76	(	(	PUNCT
ma-136	456	77	3.26	3.26	NUM
ma-136	456	78	)	)	PUNCT
ma-136	456	79	by	by	ADP
ma-136	456	80	using	use	VERB
ma-136	456	81	a	a	DET
ma-136	456	82	similar	similar	ADJ
ma-136	456	83	proof	proof	NOUN
ma-136	456	84	as	as	ADP
ma-136	456	85	in	in	ADP
ma-136	456	86	theorem	theorem	ADJ
ma-136	456	87	1.1	1.1	NUM
ma-136	456	88	or	or	CCONJ
ma-136	456	89	theorem	theorem	VERB
ma-136	456	90	1.2	1.2	NUM
ma-136	456	91	,	,	PUNCT
ma-136	456	92	we	we	PRON
ma-136	456	93	obtain	obtain	VERB
ma-136	457	1	|a0	|a0	PROPN
ma-136	457	2	(	(	PUNCT
ma-136	457	3	z)|	z)|	X
ma-136	457	4	>	>	X
ma-136	457	5	expp	expp	PROPN
ma-136	457	6	{	{	PUNCT
ma-136	457	7	γ	γ	X
ma-136	457	8	(	(	PUNCT
ma-136	457	9	logq−1	logq−1	X
ma-136	457	10	(	(	PUNCT
ma-136	457	11	1	1	NUM
ma-136	457	12	1−	1−	NUM
ma-136	457	13	|z	|z	NOUN
ma-136	457	14	|	|	ADV
ma-136	457	15	)	)	PUNCT
ma-136	457	16	)	)	PUNCT
ma-136	457	17	µ	µ	X
ma-136	457	18	}	}	PUNCT
ma-136	457	19	>	>	X
ma-136	457	20	expp	expp	PROPN
ma-136	457	21	{	{	PUNCT
ma-136	457	22	α	α	PROPN
ma-136	457	23	(	(	PUNCT
ma-136	457	24	logq−1	logq−1	X
ma-136	457	25	(	(	PUNCT
ma-136	457	26	1	1	NUM
ma-136	457	27	1−	1−	NUM
ma-136	457	28	|z	|z	NOUN
ma-136	457	29	|	|	ADV
ma-136	457	30	)	)	PUNCT
ma-136	457	31	)	)	PUNCT
ma-136	457	32	µ	µ	X
ma-136	457	33	}	}	PUNCT
ma-136	457	34	≥	≥	X
ma-136	457	35	|ai	|ai	NUM
ma-136	457	36	(	(	PUNCT
ma-136	457	37	z)|	z)|	INTJ
ma-136	457	38	(	(	PUNCT
ma-136	457	39	i	i	NOUN
ma-136	457	40	=	=	NOUN
ma-136	457	41	1	1	NUM
ma-136	457	42	,	,	PUNCT
ma-136	457	43	2	2	NUM
ma-136	457	44	,	,	PUNCT
ma-136	457	45	...	...	PUNCT
ma-136	457	46	,	,	PUNCT
ma-136	457	47	k	k	X
ma-136	457	48	)	)	PUNCT
ma-136	457	49	(	(	PUNCT
ma-136	457	50	3.27	3.27	NUM
ma-136	457	51	)	)	PUNCT
ma-136	457	52	for	for	ADP
ma-136	457	53	|z	|z	PROPN
ma-136	457	54	|	|	PROPN
ma-136	457	55	∈	∈	PROPN
ma-136	457	56	h1\e1	h1\e1	PROPN
ma-136	457	57	as	as	ADP
ma-136	457	58	|z	|z	PROPN
ma-136	457	59	|	|	PROPN
ma-136	457	60	→	→	SYM
ma-136	457	61	1−.	1−.	NUM
ma-136	457	62	applying	applying	NOUN
ma-136	457	63	(	(	PUNCT
ma-136	457	64	3.1	3.1	NUM
ma-136	457	65	)	)	PUNCT
ma-136	457	66	and	and	CCONJ
ma-136	457	67	(	(	PUNCT
ma-136	457	68	3.27	3.27	NUM
ma-136	457	69	)	)	PUNCT
ma-136	457	70	into	into	ADP
ma-136	457	71	(	(	PUNCT
ma-136	457	72	3.26	3.26	NUM
ma-136	457	73	)	)	PUNCT
ma-136	457	74	,	,	PUNCT
ma-136	457	75	we	we	PRON
ma-136	457	76	get	get	VERB
ma-136	457	77	expp	expp	ADJ
ma-136	457	78	{	{	PUNCT
ma-136	457	79	γ	γ	X
ma-136	457	80	(	(	PUNCT
ma-136	457	81	logq−1	logq−1	X
ma-136	457	82	(	(	PUNCT
ma-136	457	83	1	1	NUM
ma-136	457	84	1−	1−	NUM
ma-136	457	85	|z	|z	NOUN
ma-136	457	86	|	|	ADV
ma-136	457	87	)	)	PUNCT
ma-136	457	88	)	)	PUNCT
ma-136	457	89	µ	µ	X
ma-136	457	90	}	}	PUNCT
ma-136	457	91	≤	≤	NOUN
ma-136	457	92	|a0	|a0	PROPN
ma-136	458	1	(	(	PUNCT
ma-136	458	2	z)|	z)|	ADP
ma-136	458	3	≤	≤	PUNCT
ma-136	458	4	k	k	X
ma-136	459	1	[	[	X
ma-136	459	2	(	(	PUNCT
ma-136	459	3	1	1	NUM
ma-136	459	4	1−	1−	NUM
ma-136	459	5	|z	|z	NOUN
ma-136	459	6	|	|	ADV
ma-136	459	7	)	)	PUNCT
ma-136	459	8	2+ε	2+ε	NUM
ma-136	459	9	max	max	PROPN
ma-136	459	10	{	{	PUNCT
ma-136	459	11	log	log	NOUN
ma-136	459	12	(	(	PUNCT
ma-136	459	13	1	1	NUM
ma-136	459	14	1−	1−	NUM
ma-136	459	15	|z	|z	NOUN
ma-136	459	16	|	|	ADV
ma-136	459	17	)	)	PUNCT
ma-136	459	18	,	,	PUNCT
ma-136	459	19	t	t	PROPN
ma-136	459	20	(	(	PUNCT
ma-136	459	21	s	s	X
ma-136	459	22	(	(	PUNCT
ma-136	459	23	|z	|z	PROPN
ma-136	459	24	|	|	NOUN
ma-136	459	25	)	)	PUNCT
ma-136	459	26	,	,	PUNCT
ma-136	459	27	f	f	PROPN
ma-136	459	28	)	)	PUNCT
ma-136	459	29	}	}	PUNCT
ma-136	459	30	]	]	X
ma-136	459	31	k	k	X
ma-136	459	32	×	×	PROPN
ma-136	459	33	expp	expp	ADJ
ma-136	459	34	{	{	PUNCT
ma-136	459	35	α	α	PROPN
ma-136	459	36	(	(	PUNCT
ma-136	459	37	logq−1	logq−1	X
ma-136	459	38	(	(	PUNCT
ma-136	459	39	1	1	NUM
ma-136	459	40	1−	1−	NUM
ma-136	459	41	|z	|z	NOUN
ma-136	459	42	|	|	ADV
ma-136	459	43	)	)	PUNCT
ma-136	459	44	)	)	PUNCT
ma-136	459	45	µ	µ	X
ma-136	459	46	}	}	PUNCT
ma-136	459	47	for	for	ADP
ma-136	459	48	all	all	PRON
ma-136	459	49	z	z	NOUN
ma-136	459	50	satisfying	satisfy	VERB
ma-136	459	51	|z	|z	PROPN
ma-136	459	52	|	|	PROPN
ma-136	459	53	∈	∈	PROPN
ma-136	459	54	h1\e1	h1\e1	PROPN
ma-136	459	55	as	as	ADP
ma-136	459	56	|z	|z	PROPN
ma-136	459	57	|	|	PROPN
ma-136	459	58	→	→	SYM
ma-136	459	59	1−.	1−.	NUM
ma-136	459	60	noting	note	VERB
ma-136	459	61	that	that	SCONJ
ma-136	459	62	γ	γ	PROPN
ma-136	459	63	>	>	X
ma-136	459	64	α	α	PROPN
ma-136	459	65	,	,	PUNCT
ma-136	459	66	by	by	ADP
ma-136	459	67	the	the	DET
ma-136	459	68	last	last	ADJ
ma-136	459	69	inequality	inequality	NOUN
ma-136	459	70	,	,	PUNCT
ma-136	459	71	we	we	PRON
ma-136	459	72	have	have	VERB
ma-136	459	73	exp	exp	NOUN
ma-136	459	74	(	(	PUNCT
ma-136	459	75	(	(	PUNCT
ma-136	459	76	1−	1−	NUM
ma-136	459	77	o	o	NOUN
ma-136	459	78	(	(	PUNCT
ma-136	459	79	1	1	NUM
ma-136	459	80	)	)	PUNCT
ma-136	459	81	)	)	PUNCT
ma-136	460	1	expp−1	expp−1	NOUN
ma-136	460	2	{	{	PUNCT
ma-136	460	3	γ	γ	X
ma-136	460	4	(	(	PUNCT
ma-136	460	5	logq−1	logq−1	X
ma-136	460	6	(	(	PUNCT
ma-136	460	7	1	1	NUM
ma-136	460	8	1−	1−	NUM
ma-136	460	9	|z	|z	NOUN
ma-136	460	10	|	|	ADV
ma-136	460	11	)	)	PUNCT
ma-136	460	12	)	)	PUNCT
ma-136	460	13	µ	µ	X
ma-136	460	14	}	}	PUNCT
ma-136	460	15	)	)	PUNCT
ma-136	460	16	≤	≤	PUNCT
ma-136	461	1	k	k	X
ma-136	461	2	(	(	PUNCT
ma-136	461	3	1	1	NUM
ma-136	461	4	1−	1−	NUM
ma-136	461	5	|z	|z	NOUN
ma-136	461	6	|	|	ADV
ma-136	461	7	)	)	PUNCT
ma-136	461	8	k(2+ε	k(2+ε	PROPN
ma-136	461	9	)	)	PUNCT
ma-136	462	1	t	t	PROPN
ma-136	462	2	k	k	X
ma-136	462	3	(	(	PUNCT
ma-136	462	4	s	s	X
ma-136	462	5	(	(	PUNCT
ma-136	462	6	|z	|z	PROPN
ma-136	462	7	|	|	NOUN
ma-136	462	8	)	)	PUNCT
ma-136	462	9	,	,	PUNCT
ma-136	462	10	f	f	PROPN
ma-136	462	11	)	)	PUNCT
ma-136	462	12	(	(	PUNCT
ma-136	462	13	3.28	3.28	NUM
ma-136	462	14	)	)	PUNCT
ma-136	462	15	https://doi.org/10.28924/ada/ma.3.10	https://doi.org/10.28924/ada/ma.3.10	ADV
ma-136	462	16	eur	eur	PROPN
ma-136	462	17	.	.	PUNCT
ma-136	463	1	j.	j.	PROPN
ma-136	463	2	math	math	PROPN
ma-136	463	3	.	.	PUNCT
ma-136	464	1	anal	anal	PROPN
ma-136	464	2	.	.	PUNCT
ma-136	465	1	10.28924	10.28924	NUM
ma-136	465	2	/	/	SYM
ma-136	465	3	ada	ada	NOUN
ma-136	465	4	/	/	PROPN
ma-136	465	5	ma.3.10	ma.3.10	NOUN
ma-136	465	6	18for	18for	PROPN
ma-136	465	7	all	all	DET
ma-136	465	8	z	z	NOUN
ma-136	465	9	satisfying	satisfy	VERB
ma-136	465	10	|z	|z	PROPN
ma-136	465	11	|	|	PROPN
ma-136	465	12	∈	∈	PROPN
ma-136	465	13	h1\e1	h1\e1	PROPN
ma-136	465	14	as	as	ADP
ma-136	465	15	|z	|z	PROPN
ma-136	465	16	|	|	PROPN
ma-136	465	17	→	→	SYM
ma-136	465	18	1−.	1−.	NOUN
ma-136	465	19	then	then	ADV
ma-136	465	20	,	,	PUNCT
ma-136	465	21	by	by	ADP
ma-136	465	22	(	(	PUNCT
ma-136	465	23	3.28	3.28	NUM
ma-136	465	24	)	)	PUNCT
ma-136	465	25	and	and	CCONJ
ma-136	465	26	combining	combine	VERB
ma-136	465	27	with	with	ADP
ma-136	465	28	lemma	lemma	PROPN
ma-136	465	29	2.3	2.3	NUM
ma-136	465	30	,	,	PUNCT
ma-136	465	31	weget	weget	VERB
ma-136	465	32	for	for	ADP
ma-136	465	33	all	all	PRON
ma-136	465	34	r	r	NOUN
ma-136	465	35	=	=	PUNCT
ma-136	465	36	|z	|z	PROPN
ma-136	465	37	|	|	ADV
ma-136	465	38	∈	∈	PROPN
ma-136	465	39	h1	h1	PROPN
ma-136	465	40	exp	exp	X
ma-136	465	41	(	(	PUNCT
ma-136	465	42	(	(	PUNCT
ma-136	465	43	1−	1−	NUM
ma-136	465	44	o(1	o(1	NOUN
ma-136	465	45	)	)	PUNCT
ma-136	465	46	)	)	PUNCT
ma-136	466	1	expp−1	expp−1	NOUN
ma-136	466	2	{	{	PUNCT
ma-136	466	3	γ	γ	X
ma-136	466	4	(	(	PUNCT
ma-136	466	5	logq−1	logq−1	X
ma-136	466	6	(	(	PUNCT
ma-136	466	7	1	1	NUM
ma-136	466	8	1−	1−	NUM
ma-136	466	9	r	r	NOUN
ma-136	466	10	)	)	PUNCT
ma-136	466	11	)	)	PUNCT
ma-136	466	12	µ	µ	X
ma-136	466	13	}	}	PUNCT
ma-136	466	14	)	)	PUNCT
ma-136	466	15	≤	≤	PUNCT
ma-136	467	1	k	k	X
ma-136	467	2	(	(	PUNCT
ma-136	467	3	1	1	NUM
ma-136	467	4	1−	1−	NUM
ma-136	467	5	s	s	X
ma-136	467	6	(	(	PUNCT
ma-136	467	7	r	r	NOUN
ma-136	467	8	)	)	PUNCT
ma-136	467	9	)	)	PUNCT
ma-136	467	10	k(2+ε	k(2+ε	PROPN
ma-136	467	11	)	)	PUNCT
ma-136	468	1	t	t	PROPN
ma-136	468	2	k	k	PROPN
ma-136	468	3	(	(	PUNCT
ma-136	468	4	s1	s1	NOUN
ma-136	468	5	(	(	PUNCT
ma-136	468	6	r	r	NOUN
ma-136	468	7	)	)	PUNCT
ma-136	468	8	,	,	PUNCT
ma-136	468	9	f	f	PROPN
ma-136	468	10	)	)	PUNCT
ma-136	468	11	,	,	PUNCT
ma-136	468	12	(	(	PUNCT
ma-136	468	13	3.29	3.29	NUM
ma-136	468	14	)	)	PUNCT
ma-136	468	15	where	where	SCONJ
ma-136	468	16	s1	s1	NOUN
ma-136	468	17	(	(	PUNCT
ma-136	468	18	r	r	NOUN
ma-136	468	19	)	)	PUNCT
ma-136	468	20	=	=	SYM
ma-136	468	21	1−	1−	NUM
ma-136	468	22	d2	d2	PROPN
ma-136	468	23	(	(	PUNCT
ma-136	468	24	1−	1−	NUM
ma-136	468	25	r	r	NOUN
ma-136	468	26	)	)	PUNCT
ma-136	468	27	with	with	ADP
ma-136	468	28	d	d	PROPN
ma-136	468	29	∈	∈	PROPN
ma-136	468	30	(	(	PUNCT
ma-136	468	31	0	0	NUM
ma-136	468	32	,	,	PUNCT
ma-136	468	33	1	1	NUM
ma-136	468	34	)	)	PUNCT
ma-136	468	35	.	.	PUNCT
ma-136	469	1	therefore	therefore	ADV
ma-136	469	2	,	,	PUNCT
ma-136	469	3	from	from	ADP
ma-136	469	4	(	(	PUNCT
ma-136	469	5	3.29	3.29	NUM
ma-136	469	6	)	)	PUNCT
ma-136	469	7	we	we	PRON
ma-136	469	8	obtain	obtain	VERB
ma-136	469	9	σ[p	σ[p	NOUN
ma-136	469	10	,	,	PUNCT
ma-136	469	11	q	q	X
ma-136	469	12	]	]	X
ma-136	469	13	(	(	PUNCT
ma-136	469	14	f	f	X
ma-136	469	15	)	)	PUNCT
ma-136	470	1	=	=	NOUN
ma-136	470	2	∞	∞	NOUN
ma-136	470	3	and	and	CCONJ
ma-136	470	4	σ[p+1,q	σ[p+1,q	NOUN
ma-136	470	5	]	]	PUNCT
ma-136	470	6	(	(	PUNCT
ma-136	470	7	f	f	X
ma-136	470	8	)	)	PUNCT
ma-136	471	1	=	=	SYM
ma-136	471	2	lim	lim	PROPN
ma-136	471	3	sup	sup	PROPN
ma-136	471	4	s1(r)→1−	s1(r)→1−	PROPN
ma-136	471	5	log+p+1	log+p+1	PROPN
ma-136	471	6	t	t	PROPN
ma-136	471	7	(	(	PUNCT
ma-136	471	8	s1	s1	PROPN
ma-136	471	9	(	(	PUNCT
ma-136	471	10	r	r	NOUN
ma-136	471	11	)	)	PUNCT
ma-136	471	12	,	,	PUNCT
ma-136	471	13	f	f	X
ma-136	471	14	)	)	PUNCT
ma-136	471	15	logq	logq	NOUN
ma-136	471	16	(	(	PUNCT
ma-136	471	17	1	1	NUM
ma-136	471	18	1−s1(r	1−s1(r	NUM
ma-136	471	19	)	)	PUNCT
ma-136	471	20	)	)	PUNCT
ma-136	472	1	≥	≥	X
ma-136	472	2	µ.	µ.	NOUN
ma-136	472	3	proof	proof	NOUN
ma-136	472	4	of	of	ADP
ma-136	472	5	theorems	theorem	NOUN
ma-136	472	6	1.7	1.7	NUM
ma-136	472	7	and	and	CCONJ
ma-136	472	8	1.8	1.8	NUM
ma-136	472	9	.	.	PUNCT
ma-136	472	10	suppose	suppose	VERB
ma-136	472	11	that	that	SCONJ
ma-136	472	12	every	every	DET
ma-136	472	13	meromorphic	meromorphic	ADJ
ma-136	472	14	(	(	PUNCT
ma-136	472	15	or	or	CCONJ
ma-136	472	16	analytic	analytic	ADJ
ma-136	472	17	)	)	PUNCT
ma-136	472	18	solution	solution	NOUN
ma-136	472	19	f	f	PROPN
ma-136	472	20	ofequation	ofequation	NOUN
ma-136	472	21	(	(	PUNCT
ma-136	472	22	1.2	1.2	NUM
ma-136	472	23	)	)	PUNCT
ma-136	472	24	not	not	PART
ma-136	472	25	being	be	AUX
ma-136	472	26	identically	identically	ADV
ma-136	472	27	equal	equal	ADJ
ma-136	472	28	to	to	ADP
ma-136	472	29	0	0	NUM
ma-136	472	30	.	.	PUNCT
ma-136	473	1	by	by	ADP
ma-136	473	2	(	(	PUNCT
ma-136	473	3	1.2	1.2	NUM
ma-136	473	4	)	)	PUNCT
ma-136	473	5	,	,	PUNCT
ma-136	473	6	we	we	PRON
ma-136	473	7	can	can	AUX
ma-136	473	8	write	write	VERB
ma-136	473	9	−	−	PROPN
ma-136	473	10	a0	a0	PROPN
ma-136	473	11	(	(	PUNCT
ma-136	473	12	z	z	NOUN
ma-136	473	13	)	)	PUNCT
ma-136	473	14	=	=	SYM
ma-136	473	15	ak	ak	PROPN
ma-136	473	16	(	(	PUNCT
ma-136	473	17	z	z	PROPN
ma-136	473	18	)	)	PUNCT
ma-136	473	19	f	f	NOUN
ma-136	473	20	(	(	PUNCT
ma-136	473	21	k)(z	k)(z	NOUN
ma-136	473	22	)	)	PUNCT
ma-136	473	23	f	f	NOUN
ma-136	473	24	(	(	PUNCT
ma-136	473	25	z	z	NOUN
ma-136	473	26	)	)	PUNCT
ma-136	473	27	+	+	CCONJ
ma-136	473	28	ak−1	ak−1	ADV
ma-136	473	29	(	(	PUNCT
ma-136	473	30	z	z	NOUN
ma-136	473	31	)	)	PUNCT
ma-136	473	32	f	f	PROPN
ma-136	473	33	(	(	PUNCT
ma-136	473	34	k−1)(z	k−1)(z	PROPN
ma-136	473	35	)	)	PUNCT
ma-136	473	36	f	f	PROPN
ma-136	473	37	(	(	PUNCT
ma-136	473	38	z	z	NOUN
ma-136	473	39	)	)	PUNCT
ma-136	474	1	+	+	CCONJ
ma-136	474	2	·	·	PUNCT
ma-136	474	3	·	·	PUNCT
ma-136	474	4	·	·	PUNCT
ma-136	474	5	+	+	NUM
ma-136	474	6	a1	a1	NOUN
ma-136	474	7	(	(	PUNCT
ma-136	474	8	z	z	NOUN
ma-136	474	9	)	)	PUNCT
ma-136	474	10	f	f	PROPN
ma-136	474	11	′(z	′(z	NOUN
ma-136	474	12	)	)	PUNCT
ma-136	474	13	f	f	PROPN
ma-136	474	14	(	(	PUNCT
ma-136	474	15	z	z	NOUN
ma-136	474	16	)	)	PUNCT
ma-136	474	17	.	.	PUNCT
ma-136	475	1	(	(	PUNCT
ma-136	475	2	3.30	3.30	NUM
ma-136	475	3	)	)	PUNCT
ma-136	475	4	from	from	ADP
ma-136	475	5	(	(	PUNCT
ma-136	475	6	3.30	3.30	NUM
ma-136	475	7	)	)	PUNCT
ma-136	475	8	,	,	PUNCT
ma-136	475	9	we	we	PRON
ma-136	475	10	have	have	VERB
ma-136	475	11	t	t	NOUN
ma-136	475	12	(	(	PUNCT
ma-136	475	13	r	r	NOUN
ma-136	475	14	,	,	PUNCT
ma-136	475	15	a0	a0	NOUN
ma-136	475	16	)	)	PUNCT
ma-136	475	17	=	=	SYM
ma-136	475	18	m(r	m(r	PROPN
ma-136	475	19	,	,	PUNCT
ma-136	475	20	a0	a0	NOUN
ma-136	475	21	)	)	PUNCT
ma-136	475	22	≤	≤	PROPN
ma-136	476	1	k∑	k∑	VERB
ma-136	476	2	i=1	i=1	PROPN
ma-136	476	3	m(r	m(r	PROPN
ma-136	476	4	,	,	PUNCT
ma-136	476	5	ai	ai	VERB
ma-136	476	6	)	)	PUNCT
ma-136	476	7	+	+	CCONJ
ma-136	476	8	k∑	k∑	VERB
ma-136	476	9	i=1	i=1	INTJ
ma-136	476	10	m	m	VERB
ma-136	476	11	(	(	PUNCT
ma-136	476	12	r	r	NOUN
ma-136	476	13	,	,	PUNCT
ma-136	476	14	f	f	PROPN
ma-136	476	15	(	(	PUNCT
ma-136	476	16	i	i	NOUN
ma-136	476	17	)	)	PUNCT
ma-136	476	18	f	f	PROPN
ma-136	476	19	)	)	PUNCT
ma-136	477	1	+	+	NOUN
ma-136	477	2	o(1	o(1	NOUN
ma-136	477	3	)	)	PUNCT
ma-136	477	4	=	=	VERB
ma-136	477	5	k∑	k∑	PROPN
ma-136	477	6	i=1	i=1	PROPN
ma-136	477	7	t	t	PROPN
ma-136	477	8	(	(	PUNCT
ma-136	477	9	r	r	NOUN
ma-136	477	10	,	,	PUNCT
ma-136	477	11	ai	ai	VERB
ma-136	477	12	)	)	PUNCT
ma-136	477	13	+	+	CCONJ
ma-136	477	14	k∑	k∑	VERB
ma-136	477	15	i=1	i=1	INTJ
ma-136	477	16	m	m	VERB
ma-136	477	17	(	(	PUNCT
ma-136	477	18	r	r	NOUN
ma-136	477	19	,	,	PUNCT
ma-136	477	20	f	f	PROPN
ma-136	477	21	(	(	PUNCT
ma-136	477	22	i	i	NOUN
ma-136	477	23	)	)	PUNCT
ma-136	477	24	f	f	PROPN
ma-136	477	25	)	)	PUNCT
ma-136	478	1	+	+	NOUN
ma-136	478	2	o(1	o(1	NOUN
ma-136	478	3	)	)	PUNCT
ma-136	478	4	.	.	PUNCT
ma-136	479	1	(	(	PUNCT
ma-136	479	2	3.31	3.31	NUM
ma-136	479	3	)	)	PUNCT
ma-136	479	4	if	if	SCONJ
ma-136	479	5	p	p	PROPN
ma-136	479	6	≥	≥	PUNCT
ma-136	479	7	q	q	X
ma-136	479	8	≥	≥	NUM
ma-136	479	9	2	2	NUM
ma-136	479	10	,	,	PUNCT
ma-136	479	11	then	then	ADV
ma-136	479	12	by	by	ADP
ma-136	479	13	using	use	VERB
ma-136	479	14	a	a	DET
ma-136	479	15	similar	similar	ADJ
ma-136	479	16	proof	proof	NOUN
ma-136	479	17	as	as	ADP
ma-136	479	18	in	in	ADP
ma-136	479	19	theorem	theorem	ADJ
ma-136	479	20	1.3	1.3	NUM
ma-136	479	21	or	or	CCONJ
ma-136	479	22	theorem	theorem	VERB
ma-136	479	23	1.4	1.4	NUM
ma-136	479	24	,	,	PUNCT
ma-136	479	25	we	we	PRON
ma-136	479	26	obtain	obtain	VERB
ma-136	479	27	t	t	NOUN
ma-136	479	28	(	(	PUNCT
ma-136	479	29	r	r	NOUN
ma-136	479	30	,	,	PUNCT
ma-136	479	31	a0	a0	NOUN
ma-136	479	32	)	)	PUNCT
ma-136	479	33	>	>	X
ma-136	480	1	expp−1	expp−1	NOUN
ma-136	480	2	{	{	PUNCT
ma-136	480	3	γ	γ	X
ma-136	480	4	(	(	PUNCT
ma-136	480	5	logq−1	logq−1	X
ma-136	480	6	(	(	PUNCT
ma-136	480	7	1	1	NUM
ma-136	480	8	1−	1−	NUM
ma-136	480	9	|z	|z	NOUN
ma-136	480	10	|	|	ADV
ma-136	480	11	)	)	PUNCT
ma-136	480	12	)	)	PUNCT
ma-136	480	13	µ	µ	X
ma-136	480	14	}	}	PUNCT
ma-136	480	15	>	>	X
ma-136	480	16	expp−1	expp−1	NOUN
ma-136	480	17	{	{	PUNCT
ma-136	480	18	α	α	PROPN
ma-136	480	19	(	(	PUNCT
ma-136	480	20	logq−1	logq−1	X
ma-136	480	21	(	(	PUNCT
ma-136	480	22	1	1	NUM
ma-136	480	23	1−	1−	NUM
ma-136	480	24	|z	|z	NOUN
ma-136	480	25	|	|	ADV
ma-136	480	26	)	)	PUNCT
ma-136	480	27	)	)	PUNCT
ma-136	480	28	µ	µ	X
ma-136	480	29	}	}	PUNCT
ma-136	480	30	≥	≥	NOUN
ma-136	480	31	t	t	NOUN
ma-136	480	32	(	(	PUNCT
ma-136	480	33	r	r	NOUN
ma-136	480	34	,	,	PUNCT
ma-136	480	35	ai	ai	NOUN
ma-136	480	36	)	)	PUNCT
ma-136	480	37	,	,	PUNCT
ma-136	480	38	(	(	PUNCT
ma-136	480	39	i	i	NOUN
ma-136	480	40	=	=	NOUN
ma-136	480	41	1	1	NUM
ma-136	480	42	,	,	PUNCT
ma-136	480	43	2	2	NUM
ma-136	480	44	,	,	PUNCT
ma-136	480	45	...	...	PUNCT
ma-136	480	46	,	,	PUNCT
ma-136	480	47	k	k	X
ma-136	480	48	)	)	PUNCT
ma-136	480	49	(	(	PUNCT
ma-136	480	50	3.32	3.32	NUM
ma-136	480	51	)	)	PUNCT
ma-136	480	52	as	as	ADP
ma-136	480	53	|z	|z	PROPN
ma-136	480	54	|	|	PROPN
ma-136	480	55	→	→	SYM
ma-136	480	56	1−	1−	NUM
ma-136	480	57	for	for	ADP
ma-136	480	58	z	z	PROPN
ma-136	480	59	∈	∈	PROPN
ma-136	480	60	h.	h.	NOUN
ma-136	480	61	by	by	ADP
ma-136	480	62	applying	apply	VERB
ma-136	480	63	lemma	lemma	PROPN
ma-136	480	64	2.2	2.2	NUM
ma-136	480	65	and	and	CCONJ
ma-136	480	66	substituting	substitute	VERB
ma-136	480	67	(	(	PUNCT
ma-136	480	68	3.32	3.32	NUM
ma-136	480	69	)	)	PUNCT
ma-136	480	70	into	into	ADP
ma-136	480	71	(	(	PUNCT
ma-136	480	72	3.31	3.31	NUM
ma-136	480	73	)	)	PUNCT
ma-136	480	74	,	,	PUNCT
ma-136	480	75	we	we	PRON
ma-136	480	76	get	get	VERB
ma-136	480	77	expp−1	expp−1	NOUN
ma-136	480	78	{	{	PUNCT
ma-136	480	79	γ	γ	X
ma-136	480	80	(	(	PUNCT
ma-136	480	81	logq−1	logq−1	X
ma-136	480	82	(	(	PUNCT
ma-136	480	83	1	1	NUM
ma-136	480	84	1−	1−	NUM
ma-136	480	85	r	r	NOUN
ma-136	480	86	)	)	PUNCT
ma-136	480	87	)	)	PUNCT
ma-136	480	88	µ	µ	X
ma-136	480	89	}	}	PUNCT
ma-136	480	90	≤	≤	NUM
ma-136	480	91	k	k	PROPN
ma-136	480	92	expp−1	expp−1	PROPN
ma-136	480	93	{	{	PUNCT
ma-136	480	94	α	α	PROPN
ma-136	480	95	(	(	PUNCT
ma-136	480	96	logq−1	logq−1	X
ma-136	480	97	(	(	PUNCT
ma-136	480	98	1	1	NUM
ma-136	480	99	1−	1−	NUM
ma-136	480	100	r	r	NOUN
ma-136	480	101	)	)	PUNCT
ma-136	480	102	)	)	PUNCT
ma-136	480	103	µ	µ	X
ma-136	480	104	}	}	PUNCT
ma-136	480	105	+	+	NOUN
ma-136	480	106	o	o	X
ma-136	481	1	(	(	PUNCT
ma-136	481	2	log+	log+	PROPN
ma-136	481	3	t	t	X
ma-136	481	4	(	(	PUNCT
ma-136	481	5	r	r	NOUN
ma-136	481	6	,	,	PUNCT
ma-136	481	7	f	f	PROPN
ma-136	481	8	)	)	PUNCT
ma-136	482	1	+	+	CCONJ
ma-136	482	2	log	log	NOUN
ma-136	482	3	(	(	PUNCT
ma-136	482	4	1	1	NUM
ma-136	482	5	1−	1−	NUM
ma-136	482	6	r	r	NOUN
ma-136	482	7	)	)	PUNCT
ma-136	482	8	)	)	PUNCT
ma-136	482	9	for	for	ADP
ma-136	482	10	all	all	DET
ma-136	482	11	z	z	NOUN
ma-136	482	12	satisfying	satisfy	VERB
ma-136	482	13	|z	|z	PROPN
ma-136	483	1	|	|	ADV
ma-136	483	2	=	=	SYM
ma-136	483	3	r	r	NOUN
ma-136	483	4	∈	∈	NOUN
ma-136	483	5	h1\e2	h1\e2	PUNCT
ma-136	483	6	as	as	ADP
ma-136	483	7	|z	|z	PROPN
ma-136	483	8	|	|	ADV
ma-136	483	9	=	=	SYM
ma-136	483	10	r	r	NOUN
ma-136	483	11	→	→	SYM
ma-136	483	12	1−.	1−.	NUM
ma-136	483	13	noting	note	VERB
ma-136	483	14	that	that	SCONJ
ma-136	483	15	γ	γ	PROPN
ma-136	483	16	>	>	X
ma-136	483	17	α	α	PROPN
ma-136	483	18	,	,	PUNCT
ma-136	483	19	by	by	ADP
ma-136	483	20	the	the	DET
ma-136	483	21	last	last	ADJ
ma-136	483	22	inequality	inequality	NOUN
ma-136	483	23	,	,	PUNCT
ma-136	483	24	we	we	PRON
ma-136	483	25	have	have	VERB
ma-136	483	26	exp	exp	NOUN
ma-136	483	27	{	{	PUNCT
ma-136	483	28	(	(	PUNCT
ma-136	483	29	1−	1−	NUM
ma-136	483	30	o	o	NOUN
ma-136	483	31	(	(	PUNCT
ma-136	483	32	1	1	NUM
ma-136	483	33	)	)	PUNCT
ma-136	483	34	)	)	PUNCT
ma-136	484	1	expp−2	expp−2	PROPN
ma-136	484	2	{	{	PUNCT
ma-136	484	3	γ	γ	X
ma-136	484	4	(	(	PUNCT
ma-136	484	5	logq−1	logq−1	X
ma-136	484	6	(	(	PUNCT
ma-136	484	7	1	1	NUM
ma-136	484	8	1−	1−	NUM
ma-136	484	9	r	r	NOUN
ma-136	484	10	)	)	PUNCT
ma-136	484	11	)	)	PUNCT
ma-136	484	12	µ	µ	X
ma-136	484	13	}	}	PUNCT
ma-136	484	14	}	}	PUNCT
ma-136	484	15	≤	≤	NOUN
ma-136	484	16	o	o	NOUN
ma-136	485	1	(	(	PUNCT
ma-136	485	2	log+	log+	PROPN
ma-136	485	3	t	t	X
ma-136	485	4	(	(	PUNCT
ma-136	485	5	r	r	NOUN
ma-136	485	6	,	,	PUNCT
ma-136	485	7	f	f	PROPN
ma-136	485	8	)	)	PUNCT
ma-136	486	1	+	+	CCONJ
ma-136	486	2	log	log	NOUN
ma-136	486	3	(	(	PUNCT
ma-136	486	4	1	1	NUM
ma-136	486	5	1−	1−	NUM
ma-136	486	6	r	r	NOUN
ma-136	486	7	)	)	PUNCT
ma-136	486	8	)	)	PUNCT
ma-136	486	9	(	(	PUNCT
ma-136	486	10	3.33	3.33	NUM
ma-136	486	11	)	)	PUNCT
ma-136	486	12	for	for	ADP
ma-136	486	13	all	all	PRON
ma-136	486	14	z	z	NOUN
ma-136	486	15	satisfying	satisfy	VERB
ma-136	486	16	|z	|z	PROPN
ma-136	487	1	|	|	ADV
ma-136	487	2	=	=	SYM
ma-136	487	3	r	r	NOUN
ma-136	487	4	∈	∈	NOUN
ma-136	487	5	h1\e2	h1\e2	PUNCT
ma-136	487	6	as	as	ADP
ma-136	487	7	|z	|z	PROPN
ma-136	487	8	|	|	ADV
ma-136	487	9	=	=	SYM
ma-136	487	10	r	r	NOUN
ma-136	487	11	→	→	SYM
ma-136	487	12	1−.	1−.	PROPN
ma-136	487	13	therefore	therefore	ADV
ma-136	487	14	,	,	PUNCT
ma-136	487	15	from	from	ADP
ma-136	487	16	(	(	PUNCT
ma-136	487	17	3.33	3.33	NUM
ma-136	487	18	)	)	PUNCT
ma-136	487	19	we	we	PRON
ma-136	487	20	obtain	obtain	VERB
ma-136	487	21	σ[p	σ[p	NOUN
ma-136	487	22	,	,	PUNCT
ma-136	487	23	q	q	X
ma-136	487	24	]	]	X
ma-136	487	25	(	(	PUNCT
ma-136	487	26	f	f	X
ma-136	487	27	)	)	PUNCT
ma-136	488	1	=	=	NOUN
ma-136	488	2	∞	∞	NOUN
ma-136	488	3	and	and	CCONJ
ma-136	488	4	σ[p+1,q	σ[p+1,q	NOUN
ma-136	488	5	]	]	PUNCT
ma-136	488	6	(	(	PUNCT
ma-136	488	7	f	f	PROPN
ma-136	488	8	)	)	PUNCT
ma-136	488	9	≥	≥	PROPN
ma-136	488	10	µ.	µ.	VERB
ma-136	488	11	https://doi.org/10.28924/ada/ma.3.10	https://doi.org/10.28924/ada/ma.3.10	PROPN
ma-136	488	12	eur	eur	PROPN
ma-136	488	13	.	.	PUNCT
ma-136	489	1	j.	j.	PROPN
ma-136	489	2	math	math	PROPN
ma-136	489	3	.	.	PUNCT
ma-136	490	1	anal	anal	PROPN
ma-136	490	2	.	.	PUNCT
ma-136	491	1	10.28924	10.28924	NUM
ma-136	491	2	/	/	SYM
ma-136	491	3	ada	ada	NOUN
ma-136	491	4	/	/	PROPN
ma-136	491	5	ma.3.10	ma.3.10	NOUN
ma-136	491	6	19if	19if	NOUN
ma-136	491	7	p	p	X
ma-136	491	8	=	=	X
ma-136	491	9	q	q	NOUN
ma-136	492	1	=	=	NOUN
ma-136	492	2	1	1	NUM
ma-136	492	3	,	,	PUNCT
ma-136	492	4	then	then	ADV
ma-136	492	5	by	by	ADP
ma-136	492	6	using	use	VERB
ma-136	492	7	a	a	DET
ma-136	492	8	similar	similar	ADJ
ma-136	492	9	proof	proof	NOUN
ma-136	492	10	as	as	ADP
ma-136	492	11	in	in	ADP
ma-136	492	12	theorem	theorem	ADJ
ma-136	492	13	1.3	1.3	NUM
ma-136	492	14	or	or	CCONJ
ma-136	492	15	theorem	theorem	VERB
ma-136	492	16	1.4	1.4	NUM
ma-136	492	17	,	,	PUNCT
ma-136	492	18	we	we	PRON
ma-136	492	19	get	get	VERB
ma-136	492	20	t	t	NOUN
ma-136	492	21	(	(	PUNCT
ma-136	492	22	r	r	NOUN
ma-136	492	23	,	,	PUNCT
ma-136	492	24	a0	a0	PROPN
ma-136	492	25	)	)	PUNCT
ma-136	492	26	>	>	X
ma-136	493	1	γ	γ	X
ma-136	493	2	(	(	PUNCT
ma-136	493	3	1	1	NUM
ma-136	493	4	1−	1−	NUM
ma-136	493	5	|z	|z	PROPN
ma-136	493	6	|	|	ADV
ma-136	493	7	)	)	PUNCT
ma-136	493	8	µ	µ	X
ma-136	493	9	>	>	X
ma-136	493	10	kα	kα	X
ma-136	493	11	(	(	PUNCT
ma-136	493	12	1	1	NUM
ma-136	493	13	1−	1−	NUM
ma-136	493	14	|z	|z	PROPN
ma-136	494	1	|	|	ADV
ma-136	494	2	)	)	PUNCT
ma-136	494	3	µ	µ	X
ma-136	494	4	>	>	X
ma-136	494	5	α	α	PROPN
ma-136	494	6	(	(	PUNCT
ma-136	494	7	1	1	NUM
ma-136	494	8	1−	1−	NUM
ma-136	494	9	|z	|z	PROPN
ma-136	494	10	|	|	ADV
ma-136	494	11	)	)	PUNCT
ma-136	495	1	µ	µ	X
ma-136	495	2	≥	≥	NOUN
ma-136	495	3	t	t	PROPN
ma-136	495	4	(	(	PUNCT
ma-136	495	5	r	r	NOUN
ma-136	495	6	,	,	PUNCT
ma-136	495	7	ai	ai	NOUN
ma-136	495	8	)	)	PUNCT
ma-136	495	9	,	,	PUNCT
ma-136	495	10	(	(	PUNCT
ma-136	495	11	i	i	NOUN
ma-136	495	12	=	=	NOUN
ma-136	495	13	1	1	NUM
ma-136	495	14	,	,	PUNCT
ma-136	495	15	2	2	NUM
ma-136	495	16	,	,	PUNCT
ma-136	495	17	...	...	PUNCT
ma-136	495	18	,	,	PUNCT
ma-136	495	19	k	k	X
ma-136	495	20	)	)	PUNCT
ma-136	495	21	(	(	PUNCT
ma-136	495	22	3.34	3.34	NUM
ma-136	495	23	)	)	PUNCT
ma-136	495	24	as	as	ADP
ma-136	495	25	|z	|z	PROPN
ma-136	495	26	|	|	PROPN
ma-136	495	27	→	→	SYM
ma-136	495	28	1−	1−	NUM
ma-136	495	29	for	for	ADP
ma-136	495	30	z	z	PROPN
ma-136	495	31	∈	∈	PROPN
ma-136	495	32	h.	h.	NOUN
ma-136	495	33	by	by	ADP
ma-136	495	34	applying	apply	VERB
ma-136	495	35	lemma	lemma	PROPN
ma-136	495	36	2.2	2.2	NUM
ma-136	495	37	and	and	CCONJ
ma-136	495	38	substituting	substitute	VERB
ma-136	495	39	(	(	PUNCT
ma-136	495	40	3.34	3.34	NUM
ma-136	495	41	)	)	PUNCT
ma-136	495	42	into	into	ADP
ma-136	495	43	(	(	PUNCT
ma-136	495	44	3.31	3.31	NUM
ma-136	495	45	)	)	PUNCT
ma-136	495	46	,	,	PUNCT
ma-136	495	47	we	we	PRON
ma-136	495	48	obtain	obtain	VERB
ma-136	495	49	γ	γ	X
ma-136	495	50	(	(	PUNCT
ma-136	495	51	1	1	NUM
ma-136	495	52	1−	1−	NUM
ma-136	495	53	r	r	NOUN
ma-136	495	54	)	)	PUNCT
ma-136	495	55	µ	µ	NOUN
ma-136	495	56	≤	≤	NOUN
ma-136	495	57	kα	kα	NOUN
ma-136	495	58	(	(	PUNCT
ma-136	495	59	1	1	NUM
ma-136	495	60	1−	1−	NUM
ma-136	495	61	r	r	NOUN
ma-136	495	62	)	)	PUNCT
ma-136	495	63	µ	µ	PRON
ma-136	496	1	+	+	NOUN
ma-136	496	2	o	o	X
ma-136	496	3	(	(	PUNCT
ma-136	496	4	log+	log+	PROPN
ma-136	496	5	t	t	X
ma-136	496	6	(	(	PUNCT
ma-136	496	7	r	r	NOUN
ma-136	496	8	,	,	PUNCT
ma-136	496	9	f	f	PROPN
ma-136	496	10	)	)	PUNCT
ma-136	497	1	+	+	CCONJ
ma-136	497	2	log	log	NOUN
ma-136	497	3	(	(	PUNCT
ma-136	497	4	1	1	NUM
ma-136	497	5	1−	1−	NUM
ma-136	497	6	r	r	NOUN
ma-136	497	7	)	)	PUNCT
ma-136	497	8	)	)	PUNCT
ma-136	497	9	for	for	ADP
ma-136	497	10	all	all	DET
ma-136	497	11	z	z	NOUN
ma-136	497	12	satisfying	satisfy	VERB
ma-136	497	13	|z	|z	PROPN
ma-136	498	1	|	|	ADV
ma-136	498	2	=	=	SYM
ma-136	498	3	r	r	NOUN
ma-136	498	4	∈	∈	NOUN
ma-136	498	5	h1\e2	h1\e2	PUNCT
ma-136	498	6	as	as	ADP
ma-136	498	7	|z	|z	PROPN
ma-136	498	8	|	|	ADV
ma-136	498	9	=	=	SYM
ma-136	498	10	r	r	NOUN
ma-136	498	11	→	→	SYM
ma-136	498	12	1−.	1−.	NUM
ma-136	498	13	noting	note	VERB
ma-136	498	14	that	that	SCONJ
ma-136	498	15	γ	γ	PROPN
ma-136	498	16	>	>	X
ma-136	498	17	kα	kα	PROPN
ma-136	498	18	,	,	PUNCT
ma-136	498	19	by	by	ADP
ma-136	498	20	the	the	DET
ma-136	498	21	last	last	ADJ
ma-136	498	22	inequality	inequality	NOUN
ma-136	498	23	,	,	PUNCT
ma-136	498	24	we	we	PRON
ma-136	498	25	have	have	VERB
ma-136	498	26	(	(	PUNCT
ma-136	498	27	γ	γ	PROPN
ma-136	498	28	−	−	PROPN
ma-136	498	29	kα	kα	PROPN
ma-136	498	30	)	)	PUNCT
ma-136	498	31	(	(	PUNCT
ma-136	498	32	1	1	NUM
ma-136	498	33	1−	1−	NUM
ma-136	498	34	r	r	NOUN
ma-136	498	35	)	)	PUNCT
ma-136	499	1	µ	µ	NOUN
ma-136	499	2	≤	≤	NOUN
ma-136	500	1	o	o	NOUN
ma-136	501	1	(	(	PUNCT
ma-136	501	2	log+	log+	PROPN
ma-136	501	3	t	t	X
ma-136	501	4	(	(	PUNCT
ma-136	501	5	r	r	NOUN
ma-136	501	6	,	,	PUNCT
ma-136	501	7	f	f	PROPN
ma-136	501	8	)	)	PUNCT
ma-136	502	1	+	+	CCONJ
ma-136	502	2	log	log	NOUN
ma-136	502	3	(	(	PUNCT
ma-136	502	4	1	1	NUM
ma-136	502	5	1−	1−	NUM
ma-136	502	6	r	r	NOUN
ma-136	502	7	)	)	PUNCT
ma-136	502	8	)	)	PUNCT
ma-136	502	9	(	(	PUNCT
ma-136	502	10	3.35	3.35	NUM
ma-136	502	11	)	)	PUNCT
ma-136	502	12	for	for	ADP
ma-136	502	13	all	all	PRON
ma-136	502	14	z	z	NOUN
ma-136	502	15	satisfying	satisfy	VERB
ma-136	502	16	|z	|z	PROPN
ma-136	503	1	|	|	ADV
ma-136	503	2	=	=	SYM
ma-136	503	3	r	r	NOUN
ma-136	503	4	∈	∈	NOUN
ma-136	503	5	h1\e2	h1\e2	PUNCT
ma-136	503	6	as	as	ADP
ma-136	503	7	|z	|z	PROPN
ma-136	503	8	|	|	ADV
ma-136	503	9	=	=	SYM
ma-136	503	10	r	r	NOUN
ma-136	503	11	→	→	SYM
ma-136	503	12	1−.	1−.	PROPN
ma-136	503	13	therefore	therefore	ADV
ma-136	503	14	,	,	PUNCT
ma-136	503	15	from	from	ADP
ma-136	503	16	(	(	PUNCT
ma-136	503	17	3.35	3.35	NUM
ma-136	503	18	)	)	PUNCT
ma-136	503	19	we	we	PRON
ma-136	503	20	obtain	obtain	VERB
ma-136	503	21	σ	σ	PROPN
ma-136	503	22	(	(	PUNCT
ma-136	503	23	f	f	PROPN
ma-136	503	24	)	)	PUNCT
ma-136	504	1	=	=	SYM
ma-136	504	2	σm	σm	X
ma-136	504	3	(	(	PUNCT
ma-136	504	4	f	f	NOUN
ma-136	504	5	)	)	PUNCT
ma-136	505	1	=	=	NOUN
ma-136	505	2	∞	∞	PROPN
ma-136	505	3	and	and	CCONJ
ma-136	505	4	σ2	σ2	PROPN
ma-136	505	5	(	(	PUNCT
ma-136	505	6	f	f	PROPN
ma-136	505	7	)	)	PUNCT
ma-136	506	1	=	=	SYM
ma-136	506	2	σm,2	σm,2	PROPN
ma-136	506	3	(	(	PUNCT
ma-136	506	4	f	f	PROPN
ma-136	506	5	)	)	PUNCT
ma-136	506	6	≥	≥	PROPN
ma-136	506	7	µ.	µ.	NOUN
ma-136	506	8	4	4	X
ma-136	506	9	.	.	PUNCT
ma-136	506	10	proof	proof	NOUN
ma-136	506	11	of	of	ADP
ma-136	506	12	theorem	theorem	ADJ
ma-136	506	13	1.9	1.9	NUM
ma-136	506	14	suppose	suppose	VERB
ma-136	506	15	that	that	SCONJ
ma-136	506	16	every	every	DET
ma-136	506	17	solution	solution	NOUN
ma-136	506	18	f	f	PROPN
ma-136	506	19	of	of	ADP
ma-136	506	20	equation	equation	NOUN
ma-136	506	21	(	(	PUNCT
ma-136	506	22	1.1	1.1	NUM
ma-136	506	23	)	)	PUNCT
ma-136	506	24	not	not	PART
ma-136	506	25	being	be	AUX
ma-136	506	26	identically	identically	ADV
ma-136	506	27	equal	equal	ADJ
ma-136	506	28	to	to	ADP
ma-136	506	29	0	0	NUM
ma-136	506	30	.	.	PUNCT
ma-136	506	31	first	first	ADJ
ma-136	506	32	step	step	NOUN
ma-136	506	33	.	.	PUNCT
ma-136	507	1	we	we	PRON
ma-136	507	2	consider	consider	VERB
ma-136	507	3	the	the	DET
ma-136	507	4	fixed	fix	VERB
ma-136	507	5	points	point	NOUN
ma-136	507	6	of	of	ADP
ma-136	507	7	f	f	PROPN
ma-136	507	8	.	.	PUNCT
ma-136	508	1	define	define	VERB
ma-136	508	2	the	the	DET
ma-136	508	3	function	function	NOUN
ma-136	508	4	g	g	NOUN
ma-136	508	5	by	by	ADP
ma-136	508	6	setting	set	VERB
ma-136	508	7	g	g	PROPN
ma-136	508	8	(	(	PUNCT
ma-136	508	9	z	z	NOUN
ma-136	508	10	)	)	PUNCT
ma-136	508	11	:	:	PUNCT
ma-136	509	1	=	=	SYM
ma-136	509	2	f	f	X
ma-136	509	3	(	(	PUNCT
ma-136	509	4	z)−	z)−	PROPN
ma-136	509	5	z	z	PROPN
ma-136	509	6	,	,	PUNCT
ma-136	509	7	z	z	PROPN
ma-136	509	8	∈	∈	PROPN
ma-136	509	9	d.	d.	NOUN
ma-136	509	10	it	it	PRON
ma-136	509	11	follows	follow	VERB
ma-136	509	12	from	from	ADP
ma-136	509	13	(	(	PUNCT
ma-136	509	14	1.1	1.1	NUM
ma-136	509	15	)	)	PUNCT
ma-136	509	16	that	that	PRON
ma-136	509	17	g(k	g(k	NOUN
ma-136	509	18	)	)	PUNCT
ma-136	509	19	+	+	CCONJ
ma-136	509	20	ak−1	ak−1	PROPN
ma-136	509	21	g	g	NOUN
ma-136	509	22	(	(	PUNCT
ma-136	509	23	k−1	k−1	PROPN
ma-136	509	24	)	)	PUNCT
ma-136	509	25	+	+	PUNCT
ma-136	509	26	·	·	PUNCT
ma-136	509	27	·	·	PUNCT
ma-136	509	28	·	·	PUNCT
ma-136	509	29	+	+	NUM
ma-136	509	30	a1	a1	NOUN
ma-136	509	31	g	g	NOUN
ma-136	509	32	′	′	NOUN
ma-136	509	33	+	+	CCONJ
ma-136	509	34	a0	a0	NOUN
ma-136	509	35	g	g	NOUN
ma-136	509	36	=	=	PUNCT
ma-136	509	37	−a1	−a1	PROPN
ma-136	509	38	−	−	PROPN
ma-136	509	39	za0	za0	NOUN
ma-136	509	40	(	(	PUNCT
ma-136	509	41	4.1	4.1	NUM
ma-136	509	42	)	)	PUNCT
ma-136	509	43	and	and	CCONJ
ma-136	509	44	by	by	ADP
ma-136	509	45	theorem	theorem	ADJ
ma-136	509	46	1.1	1.1	NUM
ma-136	509	47	or	or	CCONJ
ma-136	509	48	theorem	theorem	VERB
ma-136	509	49	1.2	1.2	NUM
ma-136	509	50	,	,	PUNCT
ma-136	509	51	we	we	PRON
ma-136	509	52	get	get	VERB
ma-136	509	53	σ[p	σ[p	NOUN
ma-136	509	54	,	,	PUNCT
ma-136	509	55	q	q	X
ma-136	509	56	]	]	X
ma-136	509	57	(	(	PUNCT
ma-136	509	58	g	g	NOUN
ma-136	509	59	)	)	PUNCT
ma-136	509	60	=	=	SYM
ma-136	510	1	σ[p	σ[p	NOUN
ma-136	510	2	,	,	PUNCT
ma-136	510	3	q	q	X
ma-136	510	4	]	]	X
ma-136	510	5	(	(	PUNCT
ma-136	510	6	f	f	X
ma-136	510	7	)	)	PUNCT
ma-136	510	8	=	=	NOUN
ma-136	510	9	∞	∞	NOUN
ma-136	510	10	,	,	PUNCT
ma-136	510	11	σ[p+1,q	σ[p+1,q	NOUN
ma-136	510	12	]	]	PUNCT
ma-136	510	13	(	(	PUNCT
ma-136	510	14	g	g	NOUN
ma-136	510	15	)	)	PUNCT
ma-136	510	16	=	=	SYM
ma-136	510	17	σ[p+1,q	σ[p+1,q	NOUN
ma-136	510	18	]	]	PUNCT
ma-136	510	19	(	(	PUNCT
ma-136	510	20	f	f	X
ma-136	510	21	)	)	PUNCT
ma-136	510	22	=	=	SYM
ma-136	510	23	µ	µ	NOUN
ma-136	510	24	,	,	PUNCT
ma-136	510	25	λ̄[p+1,q	λ̄[p+1,q	NOUN
ma-136	510	26	]	]	X
ma-136	510	27	(	(	PUNCT
ma-136	510	28	g	g	NOUN
ma-136	510	29	)	)	PUNCT
ma-136	510	30	=	=	SYM
ma-136	510	31	λ̄[p+1,q	λ̄[p+1,q	NOUN
ma-136	510	32	]	]	X
ma-136	510	33	(	(	PUNCT
ma-136	510	34	f	f	PROPN
ma-136	510	35	−	−	PROPN
ma-136	510	36	z	z	PROPN
ma-136	510	37	)	)	PUNCT
ma-136	510	38	.	.	PUNCT
ma-136	511	1	(	(	PUNCT
ma-136	511	2	4.2	4.2	NUM
ma-136	511	3	)	)	PUNCT
ma-136	511	4	now	now	ADV
ma-136	511	5	,	,	PUNCT
ma-136	511	6	we	we	PRON
ma-136	511	7	prove	prove	VERB
ma-136	511	8	that	that	SCONJ
ma-136	511	9	−a1	−a1	VERB
ma-136	511	10	−	−	PROPN
ma-136	511	11	za0	za0	NOUN
ma-136	511	12	6≡	6≡	NUM
ma-136	511	13	0	0	X
ma-136	511	14	.	.	PUNCT
ma-136	511	15	assume	assume	VERB
ma-136	511	16	that	that	SCONJ
ma-136	511	17	−a1	−a1	VERB
ma-136	511	18	−	−	PROPN
ma-136	511	19	za0	za0	PROPN
ma-136	511	20	≡	≡	PROPN
ma-136	511	21	0	0	PUNCT
ma-136	511	22	.	.	PUNCT
ma-136	512	1	clearly	clearly	ADV
ma-136	512	2	a0	a0	VERB
ma-136	512	3	6≡	6≡	NUM
ma-136	512	4	0	0	NUM
ma-136	512	5	.	.	PUNCT
ma-136	513	1	then	then	ADV
ma-136	513	2	lim	lim	PROPN
ma-136	513	3	|z	|z	PROPN
ma-136	513	4	|→1−,z∈h	|→1−,z∈h	PROPN
ma-136	513	5	∣∣∣a1a0	∣∣∣a1a0	X
ma-136	513	6	∣∣∣	∣∣∣	NOUN
ma-136	513	7	=	=	SYM
ma-136	513	8	1	1	NUM
ma-136	513	9	and	and	CCONJ
ma-136	513	10	by	by	ADP
ma-136	513	11	(	(	PUNCT
ma-136	513	12	3.4	3.4	NUM
ma-136	513	13	)	)	PUNCT
ma-136	513	14	,	,	PUNCT
ma-136	513	15	we	we	PRON
ma-136	513	16	have	have	VERB
ma-136	513	17	∣∣∣∣a1	∣∣∣∣a1	NOUN
ma-136	513	18	(	(	PUNCT
ma-136	513	19	z	z	NOUN
ma-136	513	20	)	)	PUNCT
ma-136	513	21	a0	a0	NOUN
ma-136	513	22	(	(	PUNCT
ma-136	513	23	z	z	NOUN
ma-136	513	24	)	)	PUNCT
ma-136	513	25	∣∣∣∣	∣∣∣∣	PROPN
ma-136	513	26	<	<	X
ma-136	513	27	expp	expp	PROPN
ma-136	513	28	{	{	PUNCT
ma-136	513	29	α	α	PROPN
ma-136	513	30	(	(	PUNCT
ma-136	513	31	logq−1	logq−1	X
ma-136	513	32	(	(	PUNCT
ma-136	513	33	1	1	NUM
ma-136	513	34	1−|z	1−|z	NUM
ma-136	513	35	|	|	NOUN
ma-136	513	36	)	)	PUNCT
ma-136	513	37	)	)	PUNCT
ma-136	513	38	µ	µ	X
ma-136	513	39	}	}	PUNCT
ma-136	513	40	expp	expp	ADJ
ma-136	513	41	{	{	PUNCT
ma-136	513	42	γ	γ	X
ma-136	513	43	(	(	PUNCT
ma-136	513	44	logq−1	logq−1	X
ma-136	513	45	(	(	PUNCT
ma-136	513	46	1	1	NUM
ma-136	513	47	1−|z	1−|z	NUM
ma-136	513	48	|	|	NOUN
ma-136	513	49	)	)	PUNCT
ma-136	513	50	)	)	PUNCT
ma-136	513	51	µ	µ	X
ma-136	513	52	}	}	PUNCT
ma-136	513	53	=	=	SYM
ma-136	513	54	1	1	NUM
ma-136	513	55	exp	exp	NOUN
ma-136	513	56	{	{	PUNCT
ma-136	513	57	(	(	PUNCT
ma-136	513	58	1−	1−	NUM
ma-136	513	59	o	o	NOUN
ma-136	513	60	(	(	PUNCT
ma-136	513	61	1	1	NUM
ma-136	513	62	)	)	PUNCT
ma-136	513	63	)	)	PUNCT
ma-136	514	1	expp−1	expp−1	NOUN
ma-136	514	2	{	{	PUNCT
ma-136	514	3	γ	γ	X
ma-136	514	4	(	(	PUNCT
ma-136	514	5	logq−1	logq−1	X
ma-136	514	6	(	(	PUNCT
ma-136	514	7	1	1	NUM
ma-136	514	8	1−|z	1−|z	NUM
ma-136	514	9	|	|	NOUN
ma-136	514	10	)	)	PUNCT
ma-136	514	11	)	)	PUNCT
ma-136	514	12	µ	µ	X
ma-136	514	13	}	}	PUNCT
ma-136	514	14	}	}	PUNCT
ma-136	514	15	→	→	SYM
ma-136	514	16	0	0	NUM
ma-136	514	17	https://doi.org/10.28924/ada/ma.3.10	https://doi.org/10.28924/ada/ma.3.10	PROPN
ma-136	514	18	eur	eur	NOUN
ma-136	514	19	.	.	PUNCT
ma-136	515	1	j.	j.	PROPN
ma-136	515	2	math	math	PROPN
ma-136	515	3	.	.	PUNCT
ma-136	516	1	anal	anal	PROPN
ma-136	516	2	.	.	PUNCT
ma-136	517	1	10.28924	10.28924	NUM
ma-136	517	2	/	/	SYM
ma-136	517	3	ada	ada	NOUN
ma-136	517	4	/	/	NOUN
ma-136	517	5	ma.3.10	ma.3.10	ADJ
ma-136	517	6	20	20	NUM
ma-136	517	7	as	as	ADP
ma-136	517	8	|z	|z	PROPN
ma-136	517	9	|	|	PROPN
ma-136	517	10	→	→	SYM
ma-136	517	11	1−	1−	NUM
ma-136	517	12	for	for	ADP
ma-136	517	13	z	z	PROPN
ma-136	517	14	∈	∈	PROPN
ma-136	517	15	h.	h.	NOUN
ma-136	517	16	then	then	ADV
ma-136	517	17	lim	lim	PROPN
ma-136	517	18	|z	|z	PROPN
ma-136	517	19	|→1−,z∈h	|→1−,z∈h	PROPN
ma-136	517	20	∣∣∣a1a0	∣∣∣a1a0	X
ma-136	517	21	∣∣∣	∣∣∣	X
ma-136	517	22	=	=	SYM
ma-136	517	23	0	0	X
ma-136	517	24	.	.	PUNCT
ma-136	518	1	it	it	PRON
ma-136	518	2	is	be	AUX
ma-136	518	3	easy	easy	ADJ
ma-136	518	4	to	to	PART
ma-136	518	5	see	see	VERB
ma-136	518	6	the	the	DET
ma-136	518	7	contradiction	contradiction	NOUN
ma-136	518	8	.	.	PUNCT
ma-136	519	1	hence	hence	ADV
ma-136	519	2	,	,	PUNCT
ma-136	519	3	−a1	−a1	VERB
ma-136	519	4	−	−	PROPN
ma-136	519	5	za0	za0	NOUN
ma-136	519	6	6≡	6≡	NUM
ma-136	519	7	0	0	X
ma-136	519	8	.	.	PUNCT
ma-136	520	1	next	next	ADJ
ma-136	520	2	by	by	ADP
ma-136	520	3	lemma	lemma	PROPN
ma-136	520	4	2.5	2.5	NUM
ma-136	520	5	,	,	PUNCT
ma-136	520	6	we	we	PRON
ma-136	520	7	get	get	VERB
ma-136	520	8	max	max	PROPN
ma-136	520	9	{	{	PUNCT
ma-136	520	10	σ[p	σ[p	PROPN
ma-136	520	11	,	,	PUNCT
ma-136	520	12	q	q	X
ma-136	520	13	]	]	X
ma-136	520	14	(	(	PUNCT
ma-136	520	15	ai	ai	PROPN
ma-136	520	16	)	)	PUNCT
ma-136	520	17	(	(	PUNCT
ma-136	520	18	i	i	NOUN
ma-136	520	19	=	=	NOUN
ma-136	520	20	0	0	NUM
ma-136	520	21	,	,	PUNCT
ma-136	520	22	1	1	NUM
ma-136	520	23	,	,	PUNCT
ma-136	520	24	...	...	PUNCT
ma-136	520	25	,	,	PUNCT
ma-136	520	26	k	k	PROPN
ma-136	521	1	−	−	PROPN
ma-136	521	2	1	1	NUM
ma-136	521	3	)	)	PUNCT
ma-136	521	4	,	,	PUNCT
ma-136	521	5	σ[p	σ[p	PROPN
ma-136	521	6	,	,	PUNCT
ma-136	521	7	q	q	X
ma-136	521	8	]	]	X
ma-136	521	9	(	(	PUNCT
ma-136	521	10	−a1	−a1	PROPN
ma-136	521	11	−	−	PROPN
ma-136	521	12	za0	za0	NOUN
ma-136	521	13	)	)	PUNCT
ma-136	521	14	}	}	PUNCT
ma-136	522	1	<	<	X
ma-136	522	2	∞.	∞.	PROPN
ma-136	522	3	we	we	PRON
ma-136	522	4	deduce	deduce	VERB
ma-136	522	5	,	,	PUNCT
ma-136	522	6	by	by	ADP
ma-136	522	7	using	use	VERB
ma-136	522	8	(	(	PUNCT
ma-136	522	9	4.1	4.1	NUM
ma-136	522	10	)	)	PUNCT
ma-136	522	11	,	,	PUNCT
ma-136	522	12	(	(	PUNCT
ma-136	522	13	4.2	4.2	NUM
ma-136	522	14	)	)	PUNCT
ma-136	522	15	and	and	CCONJ
ma-136	522	16	lemma	lemma	PROPN
ma-136	522	17	2.6	2.6	NUM
ma-136	522	18	that	that	DET
ma-136	522	19	λ̄[p	λ̄[p	NOUN
ma-136	522	20	,	,	PUNCT
ma-136	522	21	q	q	X
ma-136	522	22	]	]	X
ma-136	522	23	(	(	PUNCT
ma-136	522	24	g	g	NOUN
ma-136	522	25	)	)	PUNCT
ma-136	523	1	=	=	SYM
ma-136	523	2	σ[p	σ[p	NOUN
ma-136	523	3	,	,	PUNCT
ma-136	523	4	q	q	X
ma-136	523	5	]	]	X
ma-136	523	6	(	(	PUNCT
ma-136	523	7	g	g	NOUN
ma-136	523	8	)	)	PUNCT
ma-136	523	9	=	=	NOUN
ma-136	523	10	∞	∞	NOUN
ma-136	523	11	,	,	PUNCT
ma-136	523	12	λ̄[p+1,q	λ̄[p+1,q	NOUN
ma-136	523	13	]	]	X
ma-136	523	14	(	(	PUNCT
ma-136	523	15	g	g	NOUN
ma-136	523	16	)	)	PUNCT
ma-136	523	17	=	=	SYM
ma-136	523	18	σ[p+1,q	σ[p+1,q	NOUN
ma-136	523	19	]	]	PUNCT
ma-136	523	20	(	(	PUNCT
ma-136	523	21	g	g	NOUN
ma-136	523	22	)	)	PUNCT
ma-136	523	23	=	=	SYM
ma-136	523	24	µ.	µ.	NOUN
ma-136	523	25	therefore	therefore	ADV
ma-136	523	26	,	,	PUNCT
ma-136	523	27	we	we	PRON
ma-136	523	28	obtain	obtain	VERB
ma-136	523	29	λ̄[p	λ̄[p	NOUN
ma-136	523	30	,	,	PUNCT
ma-136	523	31	q	q	X
ma-136	523	32	]	]	X
ma-136	523	33	(	(	PUNCT
ma-136	523	34	f	f	PROPN
ma-136	523	35	−	−	PROPN
ma-136	523	36	z	z	NOUN
ma-136	523	37	)	)	PUNCT
ma-136	523	38	=	=	NOUN
ma-136	523	39	λ̄[p	λ̄[p	NOUN
ma-136	523	40	,	,	PUNCT
ma-136	523	41	q	q	X
ma-136	523	42	]	]	X
ma-136	523	43	(	(	PUNCT
ma-136	523	44	g	g	NOUN
ma-136	523	45	)	)	PUNCT
ma-136	523	46	=	=	SYM
ma-136	524	1	σ[p	σ[p	NOUN
ma-136	524	2	,	,	PUNCT
ma-136	524	3	q	q	X
ma-136	524	4	]	]	X
ma-136	524	5	(	(	PUNCT
ma-136	524	6	g	g	NOUN
ma-136	524	7	)	)	PUNCT
ma-136	524	8	=	=	SYM
ma-136	525	1	σ[p	σ[p	NOUN
ma-136	525	2	,	,	PUNCT
ma-136	525	3	q	q	X
ma-136	525	4	]	]	X
ma-136	525	5	(	(	PUNCT
ma-136	525	6	f	f	X
ma-136	525	7	)	)	PUNCT
ma-136	525	8	=	=	NOUN
ma-136	525	9	∞	∞	NOUN
ma-136	525	10	,	,	PUNCT
ma-136	525	11	λ̄[p+1,q	λ̄[p+1,q	NOUN
ma-136	525	12	]	]	X
ma-136	525	13	(	(	PUNCT
ma-136	525	14	f	f	PROPN
ma-136	525	15	−	−	PROPN
ma-136	525	16	z	z	PROPN
ma-136	525	17	)	)	PUNCT
ma-136	525	18	=	=	SYM
ma-136	525	19	λ̄[p+1,q	λ̄[p+1,q	NOUN
ma-136	525	20	]	]	X
ma-136	525	21	(	(	PUNCT
ma-136	525	22	g	g	NOUN
ma-136	525	23	)	)	PUNCT
ma-136	525	24	=	=	SYM
ma-136	525	25	σ[p+1,q	σ[p+1,q	NOUN
ma-136	525	26	]	]	PUNCT
ma-136	525	27	(	(	PUNCT
ma-136	525	28	g	g	NOUN
ma-136	525	29	)	)	PUNCT
ma-136	525	30	=	=	SYM
ma-136	525	31	σ[p+1,q	σ[p+1,q	NOUN
ma-136	525	32	]	]	PUNCT
ma-136	525	33	(	(	PUNCT
ma-136	525	34	f	f	X
ma-136	525	35	)	)	PUNCT
ma-136	525	36	=	=	PUNCT
ma-136	526	1	µ.	µ.	NOUN
ma-136	526	2	second	second	ADJ
ma-136	526	3	step	step	NOUN
ma-136	526	4	.	.	PUNCT
ma-136	527	1	for	for	ADP
ma-136	527	2	the	the	DET
ma-136	527	3	following	following	ADJ
ma-136	527	4	proof	proof	NOUN
ma-136	527	5	,	,	PUNCT
ma-136	527	6	we	we	PRON
ma-136	527	7	use	use	VERB
ma-136	527	8	the	the	DET
ma-136	527	9	principle	principle	NOUN
ma-136	527	10	of	of	ADP
ma-136	527	11	mathematical	mathematical	ADJ
ma-136	527	12	induction	induction	NOUN
ma-136	527	13	.	.	PUNCT
ma-136	528	1	set	set	VERB
ma-136	528	2	ak	ak	PROPN
ma-136	528	3	(	(	PUNCT
ma-136	528	4	z	z	NOUN
ma-136	528	5	)	)	PUNCT
ma-136	528	6	≡	≡	PROPN
ma-136	528	7	1	1	NUM
ma-136	528	8	,	,	PUNCT
ma-136	528	9	then	then	ADV
ma-136	528	10	|ak	|ak	X
ma-136	528	11	(	(	PUNCT
ma-136	528	12	z)|	z)|	ADP
ma-136	528	13	≤	≤	NUM
ma-136	528	14	expp	expp	ADJ
ma-136	528	15	{	{	PUNCT
ma-136	528	16	α	α	PROPN
ma-136	528	17	(	(	PUNCT
ma-136	528	18	logq−1	logq−1	X
ma-136	528	19	(	(	PUNCT
ma-136	528	20	1	1	NUM
ma-136	528	21	1−	1−	NUM
ma-136	528	22	|z	|z	NOUN
ma-136	528	23	|	|	ADV
ma-136	528	24	)	)	PUNCT
ma-136	528	25	)	)	PUNCT
ma-136	528	26	µ	µ	X
ma-136	528	27	}	}	PUNCT
ma-136	528	28	and	and	CCONJ
ma-136	528	29	equation	equation	NOUN
ma-136	528	30	(	(	PUNCT
ma-136	528	31	1.1	1.1	NUM
ma-136	528	32	)	)	PUNCT
ma-136	528	33	becomes	become	VERB
ma-136	528	34	(	(	PUNCT
ma-136	528	35	1.2	1.2	NUM
ma-136	528	36	)	)	PUNCT
ma-136	528	37	.	.	PUNCT
ma-136	529	1	we	we	PRON
ma-136	529	2	consider	consider	VERB
ma-136	529	3	the	the	DET
ma-136	529	4	fixed	fix	VERB
ma-136	529	5	points	point	NOUN
ma-136	529	6	of	of	ADP
ma-136	529	7	f	f	PROPN
ma-136	529	8	(	(	PUNCT
ma-136	529	9	j	j	PROPN
ma-136	529	10	)	)	PUNCT
ma-136	529	11	(	(	PUNCT
ma-136	529	12	z	z	NOUN
ma-136	529	13	)	)	PUNCT
ma-136	529	14	(	(	PUNCT
ma-136	529	15	j	j	NOUN
ma-136	529	16	=	=	SYM
ma-136	529	17	1	1	NUM
ma-136	529	18	,	,	PUNCT
ma-136	529	19	2	2	NUM
ma-136	529	20	,	,	PUNCT
ma-136	529	21	...	...	PUNCT
ma-136	529	22	)	)	PUNCT
ma-136	529	23	.	.	PUNCT
ma-136	530	1	definethe	definethe	PRON
ma-136	530	2	function	function	NOUN
ma-136	530	3	g1	g1	NOUN
ma-136	530	4	by	by	ADP
ma-136	530	5	setting	set	VERB
ma-136	530	6	g1	g1	NOUN
ma-136	530	7	(	(	PUNCT
ma-136	530	8	z	z	NOUN
ma-136	530	9	)	)	PUNCT
ma-136	530	10	:	:	PUNCT
ma-136	531	1	=	=	PUNCT
ma-136	531	2	f	f	X
ma-136	531	3	′	′	NUM
ma-136	531	4	(	(	PUNCT
ma-136	531	5	z)−	z)−	PROPN
ma-136	531	6	z	z	PROPN
ma-136	531	7	,	,	PUNCT
ma-136	531	8	z	z	NOUN
ma-136	531	9	∈	∈	PROPN
ma-136	531	10	d.then	d.then	ADV
ma-136	531	11	,	,	PUNCT
ma-136	531	12	by	by	ADP
ma-136	531	13	lemma	lemma	PROPN
ma-136	531	14	2.5	2.5	NUM
ma-136	531	15	and	and	CCONJ
ma-136	531	16	(	(	PUNCT
ma-136	531	17	4.2	4.2	NUM
ma-136	531	18	)	)	PUNCT
ma-136	531	19	,	,	PUNCT
ma-136	531	20	we	we	PRON
ma-136	531	21	have	have	VERB
ma-136	531	22	σ[p	σ[p	NOUN
ma-136	531	23	,	,	PUNCT
ma-136	531	24	q	q	X
ma-136	531	25	]	]	X
ma-136	531	26	(	(	PUNCT
ma-136	531	27	g1	g1	PROPN
ma-136	531	28	)	)	PUNCT
ma-136	531	29	=	=	SYM
ma-136	532	1	σ[p	σ[p	NOUN
ma-136	532	2	,	,	PUNCT
ma-136	532	3	q	q	X
ma-136	532	4	]	]	X
ma-136	532	5	(	(	PUNCT
ma-136	532	6	f	f	NOUN
ma-136	532	7	′	′	NOUN
ma-136	532	8	)	)	PUNCT
ma-136	532	9	=	=	NOUN
ma-136	532	10	∞	∞	PROPN
ma-136	532	11	,	,	PUNCT
ma-136	532	12	σ[p+1,q	σ[p+1,q	NOUN
ma-136	532	13	]	]	PUNCT
ma-136	532	14	(	(	PUNCT
ma-136	532	15	g1	g1	X
ma-136	532	16	)	)	PUNCT
ma-136	532	17	=	=	SYM
ma-136	532	18	σ[p+1,q	σ[p+1,q	NOUN
ma-136	532	19	]	]	PUNCT
ma-136	532	20	(	(	PUNCT
ma-136	532	21	f	f	NOUN
ma-136	532	22	′	′	NOUN
ma-136	532	23	)	)	PUNCT
ma-136	532	24	=	=	SYM
ma-136	532	25	µ	µ	NOUN
ma-136	532	26	,	,	PUNCT
ma-136	532	27	λ̄[p+1,q	λ̄[p+1,q	NOUN
ma-136	532	28	]	]	X
ma-136	532	29	(	(	PUNCT
ma-136	532	30	g1	g1	PROPN
ma-136	532	31	)	)	PUNCT
ma-136	532	32	=	=	SYM
ma-136	532	33	λ̄[p+1,q	λ̄[p+1,q	NOUN
ma-136	532	34	]	]	X
ma-136	532	35	(	(	PUNCT
ma-136	532	36	f	f	NOUN
ma-136	532	37	′	′	NUM
ma-136	532	38	−	−	PROPN
ma-136	532	39	z	z	NOUN
ma-136	532	40	)	)	PUNCT
ma-136	532	41	.	.	PUNCT
ma-136	533	1	(	(	PUNCT
ma-136	533	2	4.3	4.3	NUM
ma-136	533	3	)	)	PUNCT
ma-136	533	4	dividing	divide	VERB
ma-136	533	5	both	both	DET
ma-136	533	6	sides	side	NOUN
ma-136	533	7	of	of	ADP
ma-136	533	8	(	(	PUNCT
ma-136	533	9	1.2	1.2	NUM
ma-136	533	10	)	)	PUNCT
ma-136	533	11	by	by	ADP
ma-136	533	12	a0	a0	PROPN
ma-136	533	13	,	,	PUNCT
ma-136	533	14	we	we	PRON
ma-136	533	15	obtain	obtain	VERB
ma-136	533	16	ak	ak	PROPN
ma-136	533	17	a0	a0	PROPN
ma-136	533	18	f	f	PROPN
ma-136	533	19	(	(	PUNCT
ma-136	533	20	k	k	NOUN
ma-136	533	21	)	)	PUNCT
ma-136	533	22	+	+	CCONJ
ma-136	533	23	ak−1	ak−1	PROPN
ma-136	533	24	a0	a0	PROPN
ma-136	533	25	f	f	PROPN
ma-136	533	26	(	(	PUNCT
ma-136	533	27	k−1	k−1	PROPN
ma-136	533	28	)	)	PUNCT
ma-136	533	29	+	+	PUNCT
ma-136	533	30	·	·	PUNCT
ma-136	533	31	·	·	PUNCT
ma-136	533	32	·	·	PUNCT
ma-136	534	1	+	+	NUM
ma-136	534	2	a1	a1	NOUN
ma-136	534	3	a0	a0	NOUN
ma-136	534	4	f	f	PROPN
ma-136	534	5	′	′	NUM
ma-136	535	1	+	+	CCONJ
ma-136	535	2	f	f	X
ma-136	535	3	=	=	SYM
ma-136	535	4	0	0	PROPN
ma-136	535	5	.	.	PUNCT
ma-136	536	1	(	(	PUNCT
ma-136	536	2	4.4	4.4	NUM
ma-136	536	3	)	)	PUNCT
ma-136	536	4	it	it	PRON
ma-136	536	5	follows	follow	VERB
ma-136	536	6	,	,	PUNCT
ma-136	536	7	by	by	ADP
ma-136	536	8	differentiating	differentiate	VERB
ma-136	536	9	both	both	DET
ma-136	536	10	sides	side	NOUN
ma-136	536	11	of	of	ADP
ma-136	536	12	equation	equation	NOUN
ma-136	536	13	(	(	PUNCT
ma-136	536	14	4.4	4.4	NUM
ma-136	536	15	)	)	PUNCT
ma-136	536	16	that	that	PRON
ma-136	536	17	ak	ak	PROPN
ma-136	536	18	a0	a0	PROPN
ma-136	536	19	f	f	PROPN
ma-136	536	20	(	(	PUNCT
ma-136	536	21	k+1	k+1	X
ma-136	536	22	)	)	PUNCT
ma-136	536	23	+	+	CCONJ
ma-136	536	24	(	(	PUNCT
ma-136	536	25	(	(	PUNCT
ma-136	536	26	ak	ak	PROPN
ma-136	536	27	a0	a0	PROPN
ma-136	536	28	)	)	PUNCT
ma-136	536	29	′	′	PROPN
ma-136	537	1	+	+	CCONJ
ma-136	537	2	ak−1	ak−1	PROPN
ma-136	537	3	a0	a0	PROPN
ma-136	537	4	)	)	PUNCT
ma-136	538	1	f	f	PROPN
ma-136	538	2	(	(	PUNCT
ma-136	538	3	k	k	NOUN
ma-136	538	4	)	)	PUNCT
ma-136	538	5	+	+	CCONJ
ma-136	538	6	·	·	PUNCT
ma-136	538	7	·	·	PUNCT
ma-136	538	8	·	·	PUNCT
ma-136	539	1	+	+	PUNCT
ma-136	539	2	(	(	PUNCT
ma-136	539	3	(	(	PUNCT
ma-136	539	4	a2	a2	PROPN
ma-136	539	5	a0	a0	PROPN
ma-136	539	6	)	)	PUNCT
ma-136	539	7	′	′	PUNCT
ma-136	540	1	+	+	CCONJ
ma-136	540	2	a1	a1	NOUN
ma-136	540	3	a0	a0	NOUN
ma-136	540	4	)	)	PUNCT
ma-136	540	5	f	f	PROPN
ma-136	541	1	′′	′′	PROPN
ma-136	541	2	+	+	CCONJ
ma-136	541	3	(	(	PUNCT
ma-136	541	4	(	(	PUNCT
ma-136	541	5	a1	a1	NOUN
ma-136	541	6	a0	a0	NOUN
ma-136	541	7	)	)	PUNCT
ma-136	541	8	′	′	NUM
ma-136	542	1	+	+	CCONJ
ma-136	542	2	1	1	X
ma-136	542	3	)	)	PUNCT
ma-136	542	4	f	f	NOUN
ma-136	542	5	′	′	NUM
ma-136	543	1	=	=	NOUN
ma-136	543	2	0	0	X
ma-136	543	3	.	.	PUNCT
ma-136	544	1	(	(	PUNCT
ma-136	544	2	4.5	4.5	NUM
ma-136	544	3	)	)	PUNCT
ma-136	544	4	multiplying	multiplying	NOUN
ma-136	544	5	(	(	PUNCT
ma-136	544	6	4.5	4.5	NUM
ma-136	544	7	)	)	PUNCT
ma-136	544	8	by	by	ADP
ma-136	544	9	a0	a0	PROPN
ma-136	544	10	,	,	PUNCT
ma-136	544	11	we	we	PRON
ma-136	544	12	have	have	VERB
ma-136	544	13	ak,1f	ak,1f	ADV
ma-136	544	14	(	(	PUNCT
ma-136	544	15	k+1	k+1	NOUN
ma-136	544	16	)	)	PUNCT
ma-136	544	17	+	+	NOUN
ma-136	544	18	ak−1,1f	ak−1,1f	NOUN
ma-136	544	19	(	(	PUNCT
ma-136	544	20	k	k	NOUN
ma-136	544	21	)	)	PUNCT
ma-136	544	22	+	+	CCONJ
ma-136	544	23	·	·	PUNCT
ma-136	544	24	·	·	PUNCT
ma-136	544	25	·	·	PUNCT
ma-136	545	1	+	+	NUM
ma-136	545	2	a1,1f	a1,1f	PROPN
ma-136	545	3	′′	′′	PROPN
ma-136	545	4	+	+	NOUN
ma-136	545	5	a0,1f	a0,1f	ADV
ma-136	545	6	′	′	NUM
ma-136	545	7	=	=	SYM
ma-136	545	8	0	0	X
ma-136	545	9	.	.	PUNCT
ma-136	546	1	(	(	PUNCT
ma-136	546	2	4.6	4.6	NUM
ma-136	546	3	)	)	PUNCT
ma-136	546	4	substituing	substitue	VERB
ma-136	546	5	f	f	NOUN
ma-136	546	6	′	′	NOUN
ma-136	546	7	=	=	PUNCT
ma-136	546	8	g1	g1	PROPN
ma-136	546	9	+	+	CCONJ
ma-136	546	10	z	z	NOUN
ma-136	546	11	into	into	ADP
ma-136	546	12	(	(	PUNCT
ma-136	546	13	4.6	4.6	NUM
ma-136	546	14	)	)	PUNCT
ma-136	546	15	,	,	PUNCT
ma-136	546	16	we	we	PRON
ma-136	546	17	obtain	obtain	VERB
ma-136	546	18	ak,1	ak,1	PROPN
ma-136	546	19	g	g	PROPN
ma-136	546	20	(	(	PUNCT
ma-136	546	21	k	k	NOUN
ma-136	546	22	)	)	PUNCT
ma-136	546	23	1	1	NUM
ma-136	547	1	+	+	CCONJ
ma-136	547	2	ak−1,1	ak−1,1	ADJ
ma-136	547	3	g	g	PROPN
ma-136	547	4	(	(	PUNCT
ma-136	547	5	k−1	k−1	PROPN
ma-136	547	6	)	)	PUNCT
ma-136	547	7	1	1	NUM
ma-136	547	8	+	+	CCONJ
ma-136	547	9	·	·	PUNCT
ma-136	547	10	·	·	PUNCT
ma-136	547	11	·	·	PUNCT
ma-136	548	1	+	+	NUM
ma-136	548	2	a1,1	a1,1	NOUN
ma-136	548	3	g	g	NOUN
ma-136	548	4	′	′	NUM
ma-136	548	5	1	1	NUM
ma-136	549	1	+	+	CCONJ
ma-136	549	2	a0,1g1	a0,1g1	PROPN
ma-136	549	3	=	=	SYM
ma-136	549	4	f1	f1	NOUN
ma-136	549	5	,	,	PUNCT
ma-136	549	6	(	(	PUNCT
ma-136	549	7	4.7	4.7	NUM
ma-136	549	8	)	)	PUNCT
ma-136	549	9	where	where	SCONJ
ma-136	549	10	ak,1	ak,1	PROPN
ma-136	549	11	=	=	SYM
ma-136	549	12	ak	ak	PROPN
ma-136	549	13	=	=	PROPN
ma-136	549	14	1	1	NUM
ma-136	549	15	,	,	PUNCT
ma-136	549	16	ai	ai	VERB
ma-136	549	17	,	,	PUNCT
ma-136	549	18	1	1	NUM
ma-136	549	19	=	=	SYM
ma-136	549	20	a0	a0	PROPN
ma-136	549	21	(	(	PUNCT
ma-136	549	22	(	(	PUNCT
ma-136	549	23	ai+1	ai+1	NUM
ma-136	549	24	a0	a0	NOUN
ma-136	549	25	)	)	PUNCT
ma-136	549	26	′	′	NUM
ma-136	550	1	+	+	CCONJ
ma-136	550	2	ai	ai	VERB
ma-136	550	3	a0	a0	PROPN
ma-136	550	4	)	)	PUNCT
ma-136	550	5	(	(	PUNCT
ma-136	550	6	i	i	NOUN
ma-136	550	7	=	=	NOUN
ma-136	550	8	1	1	NUM
ma-136	550	9	,	,	PUNCT
ma-136	550	10	2	2	NUM
ma-136	550	11	,	,	PUNCT
ma-136	550	12	...	...	PUNCT
ma-136	550	13	,	,	PUNCT
ma-136	550	14	k	k	PROPN
ma-136	551	1	−	−	PROPN
ma-136	551	2	1	1	NUM
ma-136	551	3	)	)	PUNCT
ma-136	551	4	,	,	PUNCT
ma-136	551	5	(	(	PUNCT
ma-136	551	6	4.8	4.8	NUM
ma-136	551	7	)	)	PUNCT
ma-136	551	8	https://doi.org/10.28924/ada/ma.3.10	https://doi.org/10.28924/ada/ma.3.10	ADV
ma-136	551	9	eur	eur	PROPN
ma-136	551	10	.	.	PUNCT
ma-136	552	1	j.	j.	PROPN
ma-136	552	2	math	math	PROPN
ma-136	552	3	.	.	PUNCT
ma-136	553	1	anal	anal	PROPN
ma-136	553	2	.	.	PUNCT
ma-136	554	1	10.28924	10.28924	NUM
ma-136	554	2	/	/	SYM
ma-136	554	3	ada	ada	NOUN
ma-136	554	4	/	/	SYM
ma-136	554	5	ma.3.10	ma.3.10	ADJ
ma-136	554	6	21	21	NUM
ma-136	554	7	a0,1	a0,1	PROPN
ma-136	554	8	=	=	SYM
ma-136	554	9	a0	a0	PROPN
ma-136	554	10	(	(	PUNCT
ma-136	554	11	(	(	PUNCT
ma-136	554	12	a1	a1	NOUN
ma-136	554	13	a0	a0	NOUN
ma-136	554	14	)	)	PUNCT
ma-136	554	15	′	′	NUM
ma-136	555	1	+	+	CCONJ
ma-136	555	2	1	1	NUM
ma-136	555	3	)	)	PUNCT
ma-136	555	4	,	,	PUNCT
ma-136	555	5	(	(	PUNCT
ma-136	555	6	4.9	4.9	NUM
ma-136	555	7	)	)	PUNCT
ma-136	555	8	f1	f1	NOUN
ma-136	555	9	=	=	SYM
ma-136	555	10	−	−	PROPN
ma-136	555	11	(	(	PUNCT
ma-136	555	12	a1,1	a1,1	NOUN
ma-136	555	13	+	+	CCONJ
ma-136	555	14	za0,1	za0,1	NOUN
ma-136	555	15	)	)	PUNCT
ma-136	555	16	.	.	PUNCT
ma-136	556	1	(	(	PUNCT
ma-136	556	2	4.10)next	4.10)next	NUM
ma-136	556	3	,	,	PUNCT
ma-136	556	4	we	we	PRON
ma-136	556	5	prove	prove	VERB
ma-136	556	6	that	that	SCONJ
ma-136	556	7	a0,1	a0,1	NOUN
ma-136	556	8	6≡	6≡	NUM
ma-136	556	9	0	0	NUM
ma-136	556	10	and	and	CCONJ
ma-136	556	11	f1	f1	PROPN
ma-136	556	12	6≡	6≡	NUM
ma-136	556	13	0	0	X
ma-136	556	14	.	.	PUNCT
ma-136	556	15	assume	assume	VERB
ma-136	556	16	that	that	SCONJ
ma-136	556	17	a0,1	a0,1	PROPN
ma-136	556	18	≡	≡	PROPN
ma-136	556	19	0	0	NUM
ma-136	556	20	,	,	PUNCT
ma-136	556	21	then	then	ADV
ma-136	556	22	a1	a1	NOUN
ma-136	556	23	a0	a0	NOUN
ma-136	556	24	=	=	PROPN
ma-136	556	25	−z	−z	PROPN
ma-136	556	26	+	+	CCONJ
ma-136	556	27	c0	c0	PROPN
ma-136	556	28	,	,	PUNCT
ma-136	556	29	where	where	SCONJ
ma-136	556	30	c0	c0	PROPN
ma-136	556	31	isan	isan	ADJ
ma-136	556	32	arbitrary	arbitrary	ADJ
ma-136	556	33	constant	constant	ADJ
ma-136	556	34	.	.	PUNCT
ma-136	557	1	hence	hence	ADV
ma-136	557	2	,	,	PUNCT
ma-136	557	3	we	we	PRON
ma-136	557	4	have	have	AUX
ma-136	557	5	a1	a1	NOUN
ma-136	557	6	+	+	CCONJ
ma-136	557	7	(	(	PUNCT
ma-136	557	8	z	z	NOUN
ma-136	557	9	−	−	PROPN
ma-136	557	10	c0)a0	c0)a0	NOUN
ma-136	557	11	=	=	NOUN
ma-136	557	12	0	0	NUM
ma-136	557	13	.	.	PUNCT
ma-136	558	1	then	then	ADV
ma-136	558	2	,	,	PUNCT
ma-136	558	3	f0	f0	PROPN
ma-136	558	4	=	=	SYM
ma-136	558	5	z	z	PROPN
ma-136	558	6	−	−	PROPN
ma-136	558	7	c0	c0	NOUN
ma-136	558	8	is	be	AUX
ma-136	558	9	a	a	DET
ma-136	558	10	solution	solution	NOUN
ma-136	558	11	of	of	ADP
ma-136	558	12	(	(	PUNCT
ma-136	558	13	1.1	1.1	NUM
ma-136	558	14	)	)	PUNCT
ma-136	558	15	and	and	CCONJ
ma-136	558	16	σ[p	σ[p	NOUN
ma-136	558	17	,	,	PUNCT
ma-136	558	18	q	q	X
ma-136	558	19	]	]	X
ma-136	558	20	(	(	PUNCT
ma-136	558	21	f0	f0	PROPN
ma-136	558	22	)	)	PUNCT
ma-136	558	23	<	<	X
ma-136	558	24	∞.	∞.	PROPN
ma-136	558	25	this	this	PRON
ma-136	558	26	contradicts	contradict	VERB
ma-136	558	27	(	(	PUNCT
ma-136	558	28	4.2	4.2	NUM
ma-136	558	29	)	)	PUNCT
ma-136	558	30	.	.	PUNCT
ma-136	559	1	now	now	ADV
ma-136	559	2	,	,	PUNCT
ma-136	559	3	assume	assume	VERB
ma-136	559	4	that	that	SCONJ
ma-136	559	5	f1	f1	PROPN
ma-136	559	6	≡	≡	PROPN
ma-136	559	7	0	0	NUM
ma-136	559	8	.	.	PUNCT
ma-136	560	1	by	by	ADP
ma-136	560	2	(	(	PUNCT
ma-136	560	3	4.6	4.6	NUM
ma-136	560	4	)	)	PUNCT
ma-136	560	5	and	and	CCONJ
ma-136	560	6	(	(	PUNCT
ma-136	560	7	4.10	4.10	NUM
ma-136	560	8	)	)	PUNCT
ma-136	560	9	,	,	PUNCT
ma-136	560	10	we	we	PRON
ma-136	560	11	know	know	VERB
ma-136	560	12	that	that	SCONJ
ma-136	560	13	the	the	DET
ma-136	560	14	function	function	NOUN
ma-136	560	15	f1	f1	NOUN
ma-136	560	16	such	such	ADJ
ma-136	560	17	that	that	SCONJ
ma-136	560	18	f	f	PROPN
ma-136	560	19	′1	′1	X
ma-136	560	20	=	=	SYM
ma-136	560	21	z	z	NOUN
ma-136	560	22	is	be	AUX
ma-136	560	23	a	a	DET
ma-136	560	24	solution	solution	NOUN
ma-136	560	25	of	of	ADP
ma-136	560	26	equation	equation	NOUN
ma-136	560	27	(	(	PUNCT
ma-136	560	28	4.6	4.6	NUM
ma-136	560	29	)	)	PUNCT
ma-136	560	30	and	and	CCONJ
ma-136	560	31	σ[p	σ[p	NOUN
ma-136	560	32	,	,	PUNCT
ma-136	560	33	q	q	X
ma-136	560	34	]	]	X
ma-136	560	35	(	(	PUNCT
ma-136	560	36	f1	f1	NOUN
ma-136	560	37	)	)	PUNCT
ma-136	561	1	<	<	X
ma-136	561	2	∞.this	∞.this	PROPN
ma-136	561	3	contradicts	contradict	VERB
ma-136	561	4	(	(	PUNCT
ma-136	561	5	4.2	4.2	NUM
ma-136	561	6	)	)	PUNCT
ma-136	561	7	.	.	PUNCT
ma-136	562	1	therefore	therefore	ADV
ma-136	562	2	,	,	PUNCT
ma-136	562	3	a0,1	a0,1	PROPN
ma-136	562	4	6≡	6≡	NUM
ma-136	562	5	0	0	NUM
ma-136	562	6	and	and	CCONJ
ma-136	562	7	f1	f1	PROPN
ma-136	562	8	6≡	6≡	NUM
ma-136	562	9	0	0	NUM
ma-136	562	10	.	.	PUNCT
ma-136	563	1	it	it	PRON
ma-136	563	2	follows	follow	VERB
ma-136	563	3	by	by	ADP
ma-136	563	4	(	(	PUNCT
ma-136	563	5	4.8	4.8	NUM
ma-136	563	6	)	)	PUNCT
ma-136	563	7	−	−	PROPN
ma-136	563	8	(	(	PUNCT
ma-136	563	9	4.10	4.10	NUM
ma-136	563	10	)	)	PUNCT
ma-136	563	11	and	and	CCONJ
ma-136	563	12	lemma2.5	lemma2.5	NOUN
ma-136	563	13	that	that	PRON
ma-136	563	14	max	max	PROPN
ma-136	563	15	{	{	PUNCT
ma-136	563	16	σ[p	σ[p	PROPN
ma-136	563	17	,	,	PUNCT
ma-136	563	18	q	q	X
ma-136	563	19	]	]	X
ma-136	563	20	(	(	PUNCT
ma-136	563	21	ai	ai	INTJ
ma-136	563	22	,	,	PUNCT
ma-136	563	23	1	1	NUM
ma-136	563	24	)	)	PUNCT
ma-136	563	25	(	(	PUNCT
ma-136	563	26	i	i	NOUN
ma-136	563	27	=	=	NOUN
ma-136	563	28	0	0	NUM
ma-136	563	29	,	,	PUNCT
ma-136	563	30	1	1	NUM
ma-136	563	31	,	,	PUNCT
ma-136	563	32	...	...	PUNCT
ma-136	563	33	,	,	PUNCT
ma-136	563	34	k	k	NOUN
ma-136	563	35	)	)	PUNCT
ma-136	563	36	,	,	PUNCT
ma-136	563	37	σ[p	σ[p	PROPN
ma-136	563	38	,	,	PUNCT
ma-136	563	39	q	q	X
ma-136	563	40	]	]	X
ma-136	563	41	(	(	PUNCT
ma-136	563	42	f1	f1	NOUN
ma-136	563	43	)	)	PUNCT
ma-136	563	44	}	}	PUNCT
ma-136	563	45	<	<	X
ma-136	563	46	∞.we	∞.we	X
ma-136	563	47	deduce	deduce	VERB
ma-136	563	48	by	by	ADP
ma-136	563	49	using	use	VERB
ma-136	563	50	(	(	PUNCT
ma-136	563	51	4.3	4.3	NUM
ma-136	563	52	)	)	PUNCT
ma-136	563	53	,	,	PUNCT
ma-136	563	54	(	(	PUNCT
ma-136	563	55	4.7	4.7	NUM
ma-136	563	56	)	)	PUNCT
ma-136	563	57	and	and	CCONJ
ma-136	563	58	lemma	lemma	PROPN
ma-136	563	59	2.6	2.6	NUM
ma-136	563	60	that	that	DET
ma-136	563	61	λ̄[p	λ̄[p	NOUN
ma-136	563	62	,	,	PUNCT
ma-136	563	63	q	q	X
ma-136	563	64	]	]	X
ma-136	563	65	(	(	PUNCT
ma-136	563	66	g1	g1	PROPN
ma-136	563	67	)	)	PUNCT
ma-136	564	1	=	=	SYM
ma-136	564	2	σ[p	σ[p	NOUN
ma-136	564	3	,	,	PUNCT
ma-136	564	4	q	q	X
ma-136	564	5	]	]	X
ma-136	564	6	(	(	PUNCT
ma-136	564	7	g1	g1	PROPN
ma-136	564	8	)	)	PUNCT
ma-136	564	9	=	=	SYM
ma-136	564	10	∞	∞	NOUN
ma-136	564	11	,	,	PUNCT
ma-136	564	12	λ̄[p+1,q	λ̄[p+1,q	NOUN
ma-136	564	13	]	]	X
ma-136	564	14	(	(	PUNCT
ma-136	564	15	g1	g1	PROPN
ma-136	564	16	)	)	PUNCT
ma-136	564	17	=	=	SYM
ma-136	564	18	σ[p+1,q	σ[p+1,q	NOUN
ma-136	564	19	]	]	PUNCT
ma-136	564	20	(	(	PUNCT
ma-136	564	21	g1	g1	PROPN
ma-136	564	22	)	)	PUNCT
ma-136	564	23	=	=	SYM
ma-136	564	24	µ.	µ.	NOUN
ma-136	564	25	therefore	therefore	ADV
ma-136	564	26	,	,	PUNCT
ma-136	564	27	we	we	PRON
ma-136	564	28	obtain	obtain	VERB
ma-136	564	29	λ̄[p	λ̄[p	NOUN
ma-136	564	30	,	,	PUNCT
ma-136	564	31	q	q	X
ma-136	564	32	]	]	X
ma-136	564	33	(	(	PUNCT
ma-136	564	34	f	f	NOUN
ma-136	564	35	′	′	NOUN
ma-136	565	1	−	−	PROPN
ma-136	565	2	z	z	NOUN
ma-136	565	3	)	)	PUNCT
ma-136	566	1	=	=	SYM
ma-136	566	2	λ̄[p	λ̄[p	NOUN
ma-136	566	3	,	,	PUNCT
ma-136	566	4	q	q	X
ma-136	566	5	]	]	X
ma-136	566	6	(	(	PUNCT
ma-136	566	7	g1	g1	PROPN
ma-136	566	8	)	)	PUNCT
ma-136	566	9	=	=	SYM
ma-136	566	10	σ[p	σ[p	NOUN
ma-136	566	11	,	,	PUNCT
ma-136	566	12	q	q	X
ma-136	566	13	]	]	X
ma-136	566	14	(	(	PUNCT
ma-136	566	15	g1	g1	PROPN
ma-136	566	16	)	)	PUNCT
ma-136	566	17	=	=	SYM
ma-136	566	18	σ[p	σ[p	NOUN
ma-136	566	19	,	,	PUNCT
ma-136	566	20	q	q	X
ma-136	566	21	]	]	X
ma-136	566	22	(	(	PUNCT
ma-136	566	23	f	f	X
ma-136	566	24	)	)	PUNCT
ma-136	566	25	=	=	NOUN
ma-136	566	26	∞	∞	NOUN
ma-136	566	27	,	,	PUNCT
ma-136	566	28	λ̄[p+1,q	λ̄[p+1,q	NOUN
ma-136	566	29	]	]	X
ma-136	566	30	(	(	PUNCT
ma-136	566	31	f	f	NOUN
ma-136	566	32	′	′	NOUN
ma-136	567	1	−	−	PROPN
ma-136	567	2	z	z	NOUN
ma-136	567	3	)	)	PUNCT
ma-136	567	4	=	=	SYM
ma-136	567	5	λ̄[p+1,q	λ̄[p+1,q	NOUN
ma-136	567	6	]	]	X
ma-136	567	7	(	(	PUNCT
ma-136	567	8	g1	g1	PROPN
ma-136	567	9	)	)	PUNCT
ma-136	567	10	=	=	SYM
ma-136	567	11	σ[p+1,q	σ[p+1,q	NOUN
ma-136	567	12	]	]	PUNCT
ma-136	567	13	(	(	PUNCT
ma-136	567	14	g1	g1	X
ma-136	567	15	)	)	PUNCT
ma-136	567	16	=	=	SYM
ma-136	567	17	σ[p+1,q	σ[p+1,q	NOUN
ma-136	567	18	]	]	PUNCT
ma-136	567	19	(	(	PUNCT
ma-136	567	20	f	f	X
ma-136	567	21	)	)	PUNCT
ma-136	567	22	=	=	SYM
ma-136	568	1	µ.set	µ.set	PROPN
ma-136	568	2	g2	g2	PROPN
ma-136	568	3	(	(	PUNCT
ma-136	568	4	z	z	NOUN
ma-136	568	5	)	)	PUNCT
ma-136	568	6	=	=	SYM
ma-136	568	7	f	f	X
ma-136	568	8	′′	′′	PROPN
ma-136	568	9	(	(	PUNCT
ma-136	568	10	z)−	z)−	PROPN
ma-136	568	11	z	z	PROPN
ma-136	568	12	,	,	PUNCT
ma-136	568	13	z	z	PROPN
ma-136	568	14	∈	∈	PROPN
ma-136	568	15	d.	d.	NOUN
ma-136	568	16	then	then	ADV
ma-136	568	17	,	,	PUNCT
ma-136	568	18	by	by	ADP
ma-136	568	19	using	use	VERB
ma-136	568	20	a	a	DET
ma-136	568	21	similar	similar	ADJ
ma-136	568	22	discussion	discussion	NOUN
ma-136	568	23	as	as	ADP
ma-136	568	24	in	in	ADP
ma-136	568	25	the	the	DET
ma-136	568	26	case	case	NOUN
ma-136	568	27	of	of	ADP
ma-136	568	28	the	the	DET
ma-136	568	29	function	function	NOUN
ma-136	568	30	g1	g1	NOUN
ma-136	568	31	,	,	PUNCT
ma-136	568	32	we	we	PRON
ma-136	568	33	can	can	AUX
ma-136	568	34	get	get	VERB
ma-136	568	35	ak,2f	ak,2f	PRON
ma-136	568	36	(	(	PUNCT
ma-136	568	37	k+2	k+2	NUM
ma-136	568	38	)	)	PUNCT
ma-136	568	39	+	+	NUM
ma-136	569	1	ak−1,2f	ak−1,2f	PROPN
ma-136	569	2	(	(	PUNCT
ma-136	569	3	k+1	k+1	NOUN
ma-136	569	4	)	)	PUNCT
ma-136	569	5	+	+	CCONJ
ma-136	569	6	·	·	PUNCT
ma-136	569	7	·	·	PUNCT
ma-136	569	8	·	·	PUNCT
ma-136	569	9	+	+	PUNCT
ma-136	570	1	a1,2f	a1,2f	PROPN
ma-136	570	2	(	(	PUNCT
ma-136	570	3	3	3	NUM
ma-136	570	4	)	)	PUNCT
ma-136	570	5	+	+	NUM
ma-136	570	6	a0,2f	a0,2f	PROPN
ma-136	570	7	′′	′′	PROPN
ma-136	570	8	=	=	SYM
ma-136	570	9	0and	0and	PROPN
ma-136	570	10	ak,2	ak,2	PROPN
ma-136	570	11	g	g	PROPN
ma-136	570	12	(	(	PUNCT
ma-136	570	13	k	k	NOUN
ma-136	570	14	)	)	PUNCT
ma-136	570	15	2	2	NUM
ma-136	570	16	+	+	ADP
ma-136	570	17	ak−1,2	ak−1,2	NUM
ma-136	570	18	g	g	PROPN
ma-136	570	19	(	(	PUNCT
ma-136	570	20	k−1	k−1	PROPN
ma-136	570	21	)	)	PUNCT
ma-136	570	22	2	2	NUM
ma-136	570	23	+	+	CCONJ
ma-136	570	24	·	·	PUNCT
ma-136	570	25	·	·	PUNCT
ma-136	570	26	·	·	PUNCT
ma-136	570	27	+	+	PUNCT
ma-136	570	28	a1,2	a1,2	ADJ
ma-136	570	29	g	g	NOUN
ma-136	570	30	′	′	NUM
ma-136	570	31	2	2	NUM
ma-136	570	32	+	+	NUM
ma-136	570	33	a0,2g2	a0,2g2	NUM
ma-136	570	34	=	=	SYM
ma-136	570	35	f2,where	f2,where	NOUN
ma-136	570	36	ak,2	ak,2	NOUN
ma-136	570	37	=	=	SYM
ma-136	570	38	1	1	X
ma-136	570	39	,	,	PUNCT
ma-136	570	40	ai	ai	VERB
ma-136	570	41	,	,	PUNCT
ma-136	570	42	2	2	NUM
ma-136	570	43	=	=	SYM
ma-136	570	44	a0,1	a0,1	NOUN
ma-136	570	45	(	(	PUNCT
ma-136	570	46	(	(	PUNCT
ma-136	570	47	ai+1,1	ai+1,1	INTJ
ma-136	570	48	a0,1	a0,1	NOUN
ma-136	570	49	)	)	PUNCT
ma-136	570	50	′	′	VERB
ma-136	571	1	+	+	CCONJ
ma-136	571	2	ai	ai	VERB
ma-136	571	3	,	,	PUNCT
ma-136	571	4	1	1	NUM
ma-136	571	5	a0,1	a0,1	NOUN
ma-136	571	6	)	)	PUNCT
ma-136	571	7	(	(	PUNCT
ma-136	571	8	i	i	NOUN
ma-136	571	9	=	=	NOUN
ma-136	571	10	1	1	NUM
ma-136	571	11	,	,	PUNCT
ma-136	571	12	2	2	NUM
ma-136	571	13	,	,	PUNCT
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ma-136	573	9	(	(	PUNCT
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ma-136	573	12	)	)	PUNCT
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ma-136	574	2	1	1	X
ma-136	574	3	)	)	PUNCT
ma-136	574	4	,	,	PUNCT
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ma-136	574	6	=	=	SYM
ma-136	574	7	−	−	PROPN
ma-136	574	8	(	(	PUNCT
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ma-136	574	10	+	+	NUM
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ma-136	574	12	)	)	PUNCT
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ma-136	575	1	=	=	SYM
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ma-136	575	6	(	(	PUNCT
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ma-136	575	8	)	)	PUNCT
ma-136	575	9	=	=	SYM
ma-136	576	1	σ[p	σ[p	NOUN
ma-136	576	2	,	,	PUNCT
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ma-136	576	5	(	(	PUNCT
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ma-136	576	7	)	)	PUNCT
ma-136	576	8	=	=	SYM
ma-136	577	1	σ[p	σ[p	NOUN
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ma-136	577	5	(	(	PUNCT
ma-136	577	6	f	f	X
ma-136	577	7	)	)	PUNCT
ma-136	577	8	=	=	NOUN
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ma-136	577	13	(	(	PUNCT
ma-136	577	14	f	f	X
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ma-136	577	17	z	z	NOUN
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ma-136	577	19	=	=	SYM
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ma-136	577	22	(	(	PUNCT
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ma-136	577	24	)	)	PUNCT
ma-136	577	25	=	=	SYM
ma-136	577	26	σ[p+1,q	σ[p+1,q	NOUN
ma-136	577	27	]	]	PUNCT
ma-136	577	28	(	(	PUNCT
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ma-136	577	34	(	(	PUNCT
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ma-136	577	37	=	=	SYM
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ma-136	578	8	,	,	PUNCT
ma-136	578	9	λ̄[p	λ̄[p	PROPN
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ma-136	578	13	(	(	PUNCT
ma-136	578	14	f	f	X
ma-136	578	15	(	(	PUNCT
ma-136	578	16	s	s	NOUN
ma-136	578	17	)	)	PUNCT
ma-136	578	18	−	−	PROPN
ma-136	578	19	z	z	NOUN
ma-136	578	20	)	)	PUNCT
ma-136	578	21	=	=	SYM
ma-136	579	1	σ[p	σ[p	NOUN
ma-136	579	2	,	,	PUNCT
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ma-136	579	4	]	]	X
ma-136	579	5	(	(	PUNCT
ma-136	579	6	f	f	X
ma-136	579	7	)	)	PUNCT
ma-136	579	8	=	=	NOUN
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ma-136	579	10	,	,	PUNCT
ma-136	579	11	λ̄[p+1,q	λ̄[p+1,q	NOUN
ma-136	579	12	]	]	X
ma-136	579	13	(	(	PUNCT
ma-136	579	14	f	f	X
ma-136	579	15	(	(	PUNCT
ma-136	579	16	s	s	NOUN
ma-136	579	17	)	)	PUNCT
ma-136	579	18	−	−	PROPN
ma-136	579	19	z	z	NOUN
ma-136	579	20	)	)	PUNCT
ma-136	579	21	=	=	SYM
ma-136	579	22	σ[p+1,q	σ[p+1,q	NOUN
ma-136	579	23	]	]	PUNCT
ma-136	579	24	(	(	PUNCT
ma-136	579	25	f	f	X
ma-136	579	26	)	)	PUNCT
ma-136	579	27	=	=	SYM
ma-136	579	28	µ	µ	X
ma-136	579	29	(	(	PUNCT
ma-136	579	30	4.11	4.11	NUM
ma-136	579	31	)	)	PUNCT
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ma-136	579	34	.	.	PUNCT
ma-136	580	1	j.	j.	PROPN
ma-136	580	2	math	math	PROPN
ma-136	580	3	.	.	PUNCT
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ma-136	581	2	.	.	PUNCT
ma-136	582	1	10.28924	10.28924	NUM
ma-136	582	2	/	/	SYM
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ma-136	582	4	/	/	NOUN
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ma-136	582	8	s	s	PART
ma-136	582	9	=	=	SYM
ma-136	582	10	0	0	NUM
ma-136	582	11	,	,	PUNCT
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ma-136	582	13	,	,	PUNCT
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ma-136	582	15	,	,	PUNCT
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ma-136	583	2	,	,	PUNCT
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ma-136	583	4	we	we	PRON
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ma-136	583	7	for	for	ADP
ma-136	583	8	s	s	NOUN
ma-136	583	9	=	=	VERB
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ma-136	583	13	(	(	PUNCT
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ma-136	583	15	)	)	PUNCT
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ma-136	584	3	(	(	PUNCT
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ma-136	584	5	)	)	PUNCT
ma-136	584	6	=	=	SYM
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ma-136	585	2	(	(	PUNCT
ma-136	585	3	j	j	NOUN
ma-136	585	4	)	)	PUNCT
ma-136	585	5	(	(	PUNCT
ma-136	585	6	z)−z	z)−z	PROPN
ma-136	585	7	,	,	PUNCT
ma-136	585	8	z	z	PROPN
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ma-136	585	15	(	(	PUNCT
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ma-136	585	17	)	)	PUNCT
ma-136	585	18	,	,	PUNCT
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ma-136	585	21	σ[p	σ[p	NOUN
ma-136	585	22	,	,	PUNCT
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ma-136	585	25	(	(	PUNCT
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ma-136	585	27	)	)	PUNCT
ma-136	585	28	=	=	PUNCT
ma-136	586	1	σ[p	σ[p	NOUN
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ma-136	586	5	(	(	PUNCT
ma-136	586	6	f	f	X
ma-136	586	7	(	(	PUNCT
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ma-136	586	9	)	)	PUNCT
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ma-136	587	1	=	=	SYM
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ma-136	587	3	,	,	PUNCT
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ma-136	587	6	(	(	PUNCT
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ma-136	587	8	)	)	PUNCT
ma-136	587	9	=	=	SYM
ma-136	587	10	σ[p+1,q	σ[p+1,q	NOUN
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ma-136	587	12	(	(	PUNCT
ma-136	587	13	f	f	X
ma-136	587	14	(	(	PUNCT
ma-136	587	15	j	j	PROPN
ma-136	587	16	)	)	PUNCT
ma-136	587	17	)	)	PUNCT
ma-136	587	18	=	=	SYM
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ma-136	587	20	,	,	PUNCT
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ma-136	587	23	(	(	PUNCT
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ma-136	587	25	)	)	PUNCT
ma-136	587	26	=	=	SYM
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ma-136	587	28	]	]	X
ma-136	587	29	(	(	PUNCT
ma-136	587	30	f	f	X
ma-136	587	31	(	(	PUNCT
ma-136	587	32	j	j	PROPN
ma-136	587	33	)	)	PUNCT
ma-136	587	34	−	−	PROPN
ma-136	587	35	z	z	NOUN
ma-136	587	36	)	)	PUNCT
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ma-136	588	1	(	(	PUNCT
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ma-136	588	3	)	)	PUNCT
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ma-136	588	7	same	same	ADJ
ma-136	588	8	procedure	procedure	NOUN
ma-136	588	9	as	as	ADP
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ma-136	588	11	,	,	PUNCT
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ma-136	588	17	f	f	X
ma-136	588	18	(	(	PUNCT
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ma-136	588	20	)	)	PUNCT
ma-136	589	1	+	+	CCONJ
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ma-136	589	4	(	(	PUNCT
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ma-136	589	7	+	+	CCONJ
ma-136	589	8	·	·	PUNCT
ma-136	589	9	·	·	PUNCT
ma-136	589	10	·	·	PUNCT
ma-136	589	11	+	+	NUM
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ma-136	589	13	f	f	X
ma-136	589	14	(	(	PUNCT
ma-136	589	15	j+1	j+1	PROPN
ma-136	589	16	)	)	PUNCT
ma-136	589	17	+	+	CCONJ
ma-136	590	1	a0,j	a0,j	PROPN
ma-136	590	2	f	f	PROPN
ma-136	590	3	(	(	PUNCT
ma-136	590	4	j	j	NOUN
ma-136	590	5	)	)	PUNCT
ma-136	590	6	=	=	SYM
ma-136	590	7	0	0	PUNCT
ma-136	590	8	(	(	PUNCT
ma-136	590	9	4.13	4.13	NUM
ma-136	590	10	)	)	PUNCT
ma-136	590	11	and	and	CCONJ
ma-136	590	12	ak	ak	PROPN
ma-136	590	13	,	,	PUNCT
ma-136	590	14	jg	jg	PROPN
ma-136	590	15	(	(	PUNCT
ma-136	590	16	k	k	PROPN
ma-136	590	17	)	)	PUNCT
ma-136	590	18	j	j	PROPN
ma-136	590	19	+	+	PROPN
ma-136	590	20	ak−1,jg	ak−1,jg	PROPN
ma-136	590	21	(	(	PUNCT
ma-136	590	22	k−1	k−1	PROPN
ma-136	590	23	)	)	PUNCT
ma-136	590	24	j	j	PROPN
ma-136	590	25	+	+	CCONJ
ma-136	590	26	·	·	PUNCT
ma-136	590	27	·	·	PUNCT
ma-136	590	28	·	·	PUNCT
ma-136	591	1	+	+	NUM
ma-136	591	2	a1,jg	a1,jg	NOUN
ma-136	591	3	′	′	NUM
ma-136	592	1	j	j	PROPN
ma-136	593	1	+	+	CCONJ
ma-136	593	2	a0,jgj	a0,jgj	PROPN
ma-136	593	3	=	=	SYM
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ma-136	593	5	,	,	PUNCT
ma-136	593	6	(	(	PUNCT
ma-136	593	7	4.14)where	4.14)where	NUM
ma-136	593	8	ak	ak	PROPN
ma-136	593	9	,	,	PUNCT
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ma-136	593	11	=	=	SYM
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ma-136	593	13	,	,	PUNCT
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ma-136	593	15	,	,	PUNCT
ma-136	593	16	j	j	PROPN
ma-136	593	17	=	=	NOUN
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ma-136	593	19	(	(	PUNCT
ma-136	593	20	(	(	PUNCT
ma-136	593	21	ai+1,j−1	ai+1,j−1	PROPN
ma-136	593	22	a0,j−1	a0,j−1	NOUN
ma-136	593	23	)	)	PUNCT
ma-136	593	24	′	′	NUM
ma-136	594	1	+	+	CCONJ
ma-136	594	2	ai	ai	VERB
ma-136	594	3	,	,	PUNCT
ma-136	594	4	j−1	j−1	PROPN
ma-136	594	5	a0,j−1	a0,j−1	NOUN
ma-136	594	6	)	)	PUNCT
ma-136	595	1	(	(	PUNCT
ma-136	595	2	i	i	NOUN
ma-136	595	3	=	=	NOUN
ma-136	595	4	1	1	NUM
ma-136	595	5	,	,	PUNCT
ma-136	595	6	2	2	NUM
ma-136	595	7	,	,	PUNCT
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ma-136	595	9	,	,	PUNCT
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ma-136	595	14	,	,	PUNCT
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ma-136	595	16	=	=	PUNCT
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ma-136	595	18	(	(	PUNCT
ma-136	595	19	(	(	PUNCT
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ma-136	595	21	a0,j−1	a0,j−1	NOUN
ma-136	595	22	)	)	PUNCT
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ma-136	596	1	+	+	CCONJ
ma-136	596	2	1	1	X
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ma-136	596	6	(	(	PUNCT
ma-136	596	7	a0,0	a0,0	NOUN
ma-136	596	8	=	=	SYM
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ma-136	596	10	,	,	PUNCT
ma-136	596	11	a1,0	a1,0	PROPN
ma-136	596	12	=	=	PUNCT
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ma-136	596	14	)	)	PUNCT
ma-136	596	15	,	,	PUNCT
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ma-136	596	17	=	=	PUNCT
ma-136	596	18	−	−	PROPN
ma-136	596	19	(	(	PUNCT
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ma-136	596	32	(	(	PUNCT
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ma-136	596	34	)	)	PUNCT
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ma-136	596	40	(	(	PUNCT
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ma-136	596	42	(	(	PUNCT
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ma-136	596	45	−	−	PROPN
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ma-136	597	1	=	=	SYM
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ma-136	597	6	(	(	PUNCT
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ma-136	597	8	)	)	PUNCT
ma-136	597	9	=	=	PUNCT
ma-136	598	1	σ[p	σ[p	NOUN
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ma-136	599	5	(	(	PUNCT
ma-136	599	6	f	f	X
ma-136	599	7	(	(	PUNCT
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ma-136	599	9	)	)	PUNCT
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ma-136	600	6	(	(	PUNCT
ma-136	600	7	f	f	X
ma-136	600	8	(	(	PUNCT
ma-136	600	9	j	j	PROPN
ma-136	600	10	)	)	PUNCT
ma-136	600	11	−	−	PROPN
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ma-136	601	18	(	(	PUNCT
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ma-136	602	22	(	(	PUNCT
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ma-136	602	25	−	−	PROPN
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ma-136	603	8	−	−	PROPN
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ma-136	603	11	=	=	SYM
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ma-136	603	16	(	(	PUNCT
ma-136	603	17	f	f	X
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ma-136	603	21	,	,	PUNCT
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ma-136	603	24	(	(	PUNCT
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ma-136	603	26	(	(	PUNCT
ma-136	603	27	j	j	PROPN
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ma-136	604	7	z	z	PROPN
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ma-136	604	9	=	=	SYM
ma-136	604	10	σ[p+1,q	σ[p+1,q	NOUN
ma-136	604	11	]	]	PUNCT
ma-136	604	12	(	(	PUNCT
ma-136	604	13	f	f	X
ma-136	604	14	)	)	PUNCT
ma-136	604	15	=	=	SYM
ma-136	604	16	µ	µ	X
ma-136	604	17	(	(	PUNCT
ma-136	604	18	j	j	NOUN
ma-136	604	19	=	=	SYM
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ma-136	604	21	,	,	PUNCT
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ma-136	604	23	,	,	PUNCT
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ma-136	604	25	)	)	PUNCT
ma-136	604	26	.	.	PUNCT
ma-136	605	1	5	5	X
ma-136	605	2	.	.	X
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ma-136	605	6	1.10	1.10	NUM
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ma-136	605	8	1.11	1.11	NUM
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ma-136	605	10	of	of	ADP
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ma-136	605	12	1.10	1.10	NUM
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ma-136	605	17	solution	solution	NOUN
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ma-136	605	28	0	0	NUM
ma-136	605	29	.	.	PUNCT
ma-136	605	30	by	by	ADP
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ma-136	605	35	theorem	theorem	VERB
ma-136	605	36	1.4	1.4	NUM
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ma-136	605	40	σ[p	σ[p	NOUN
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ma-136	605	42	q	q	X
ma-136	605	43	]	]	X
ma-136	605	44	(	(	PUNCT
ma-136	605	45	f	f	X
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ma-136	605	47	=	=	NOUN
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ma-136	605	49	,	,	PUNCT
ma-136	605	50	σ[p+1,q	σ[p+1,q	NOUN
ma-136	605	51	]	]	PUNCT
ma-136	605	52	(	(	PUNCT
ma-136	605	53	f	f	X
ma-136	605	54	)	)	PUNCT
ma-136	605	55	=	=	PUNCT
ma-136	606	1	µ.	µ.	NOUN
ma-136	606	2	now	now	ADV
ma-136	606	3	,	,	PUNCT
ma-136	606	4	we	we	PRON
ma-136	606	5	prove	prove	VERB
ma-136	606	6	that	that	SCONJ
ma-136	606	7	−a1	−a1	VERB
ma-136	606	8	−	−	PROPN
ma-136	606	9	za0	za0	NOUN
ma-136	606	10	6≡	6≡	NUM
ma-136	606	11	0	0	X
ma-136	606	12	.	.	PUNCT
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ma-136	606	14	that	that	SCONJ
ma-136	606	15	−a1	−a1	VERB
ma-136	606	16	−	−	PROPN
ma-136	606	17	za0	za0	PROPN
ma-136	606	18	≡	≡	PROPN
ma-136	606	19	0	0	NUM
ma-136	606	20	,	,	PUNCT
ma-136	606	21	then	then	ADV
ma-136	606	22	we	we	PRON
ma-136	606	23	can	can	AUX
ma-136	606	24	easily	easily	ADV
ma-136	606	25	obtain	obtain	VERB
ma-136	606	26	t	t	NOUN
ma-136	606	27	(	(	PUNCT
ma-136	606	28	r	r	NOUN
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ma-136	606	32	=	=	SYM
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ma-136	606	34	(	(	PUNCT
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ma-136	606	36	)	)	PUNCT
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ma-136	609	1	+	+	NUM
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ma-136	609	15	=	=	SYM
ma-136	610	1	t	t	PROPN
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ma-136	610	4	,	,	PUNCT
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ma-136	610	8	t	t	NOUN
ma-136	610	9	(	(	PUNCT
ma-136	610	10	r	r	NOUN
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ma-136	610	14	+	+	NUM
ma-136	610	15	t	t	NOUN
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ma-136	611	1	+	+	NOUN
ma-136	611	2	o	o	X
ma-136	611	3	(	(	PUNCT
ma-136	611	4	1	1	NUM
ma-136	611	5	)	)	PUNCT
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ma-136	612	1	(	(	PUNCT
ma-136	612	2	5.1	5.1	NUM
ma-136	612	3	)	)	PUNCT
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ma-136	612	7	(	(	PUNCT
ma-136	612	8	5.1	5.1	NUM
ma-136	612	9	)	)	PUNCT
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ma-136	612	12	t	t	NOUN
ma-136	612	13	(	(	PUNCT
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ma-136	613	1	+	+	NOUN
ma-136	613	2	o	o	X
ma-136	613	3	(	(	PUNCT
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ma-136	613	5	)	)	PUNCT
ma-136	613	6	t	t	NOUN
ma-136	613	7	(	(	PUNCT
ma-136	613	8	r	r	NOUN
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ma-136	613	10	a0	a0	NOUN
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ma-136	613	12	≤	≤	PROPN
ma-136	613	13	t	t	NOUN
ma-136	613	14	(	(	PUNCT
ma-136	613	15	r	r	NOUN
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ma-136	613	17	a1	a1	NOUN
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ma-136	613	19	t	t	NOUN
ma-136	613	20	(	(	PUNCT
ma-136	613	21	r	r	NOUN
ma-136	613	22	,	,	PUNCT
ma-136	613	23	a0	a0	NOUN
ma-136	613	24	)	)	PUNCT
ma-136	613	25	≤	≤	NOUN
ma-136	613	26	1	1	NUM
ma-136	614	1	+	+	NUM
ma-136	614	2	t	t	PROPN
ma-136	614	3	(	(	PUNCT
ma-136	614	4	r	r	NOUN
ma-136	614	5	,	,	PUNCT
ma-136	614	6	z	z	NOUN
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ma-136	614	8	t	t	NOUN
ma-136	614	9	(	(	PUNCT
ma-136	614	10	r	r	NOUN
ma-136	614	11	,	,	PUNCT
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ma-136	614	13	)	)	PUNCT
ma-136	614	14	.	.	PUNCT
ma-136	615	1	(	(	PUNCT
ma-136	615	2	5.2	5.2	NUM
ma-136	615	3	)	)	PUNCT
ma-136	615	4	https://doi.org/10.28924/ada/ma.3.10	https://doi.org/10.28924/ada/ma.3.10	ADV
ma-136	615	5	eur	eur	PROPN
ma-136	615	6	.	.	PUNCT
ma-136	616	1	j.	j.	PROPN
ma-136	616	2	math	math	PROPN
ma-136	616	3	.	.	PUNCT
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ma-136	617	2	.	.	PUNCT
ma-136	618	1	10.28924	10.28924	NUM
ma-136	618	2	/	/	SYM
ma-136	618	3	ada	ada	NOUN
ma-136	618	4	/	/	SYM
ma-136	618	5	ma.3.10	ma.3.10	ADJ
ma-136	618	6	23by	23by	NOUN
ma-136	618	7	following	follow	VERB
ma-136	618	8	the	the	DET
ma-136	618	9	same	same	ADJ
ma-136	618	10	reasoning	reasoning	NOUN
ma-136	618	11	as	as	ADP
ma-136	618	12	in	in	ADP
ma-136	618	13	the	the	DET
ma-136	618	14	proof	proof	NOUN
ma-136	618	15	of	of	ADP
ma-136	618	16	theorem	theorem	ADJ
ma-136	618	17	1.3	1.3	NUM
ma-136	618	18	or	or	CCONJ
ma-136	618	19	theorem	theorem	VERB
ma-136	618	20	1.4	1.4	NUM
ma-136	618	21	,	,	PUNCT
ma-136	618	22	we	we	PRON
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ma-136	618	24	t	t	NOUN
ma-136	618	25	(	(	PUNCT
ma-136	618	26	r	r	NOUN
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ma-136	618	28	a0	a0	NOUN
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ma-136	618	30	>	>	X
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ma-136	619	2	{	{	PUNCT
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ma-136	619	4	(	(	PUNCT
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ma-136	619	6	(	(	PUNCT
ma-136	619	7	1	1	NUM
ma-136	619	8	1−	1−	NUM
ma-136	619	9	|z	|z	NOUN
ma-136	619	10	|	|	ADV
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ma-136	619	12	)	)	PUNCT
ma-136	619	13	µ	µ	X
ma-136	619	14	}	}	PUNCT
ma-136	619	15	>	>	X
ma-136	619	16	expp−1	expp−1	NOUN
ma-136	619	17	{	{	PUNCT
ma-136	619	18	α	α	PROPN
ma-136	619	19	(	(	PUNCT
ma-136	619	20	logq−1	logq−1	X
ma-136	619	21	(	(	PUNCT
ma-136	619	22	1	1	NUM
ma-136	619	23	1−	1−	NUM
ma-136	619	24	|z	|z	NOUN
ma-136	619	25	|	|	ADV
ma-136	619	26	)	)	PUNCT
ma-136	619	27	)	)	PUNCT
ma-136	619	28	µ	µ	X
ma-136	619	29	}	}	PUNCT
ma-136	619	30	≥	≥	NOUN
ma-136	619	31	t	t	NOUN
ma-136	619	32	(	(	PUNCT
ma-136	619	33	r	r	NOUN
ma-136	619	34	,	,	PUNCT
ma-136	619	35	a1	a1	NOUN
ma-136	619	36	)	)	PUNCT
ma-136	619	37	(	(	PUNCT
ma-136	619	38	5.3	5.3	NUM
ma-136	619	39	)	)	PUNCT
ma-136	619	40	as	as	ADP
ma-136	619	41	r	r	NOUN
ma-136	619	42	=	=	PUNCT
ma-136	619	43	|z	|z	PROPN
ma-136	619	44	|	|	PROPN
ma-136	619	45	→	→	SYM
ma-136	619	46	1−	1−	NUM
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ma-136	619	48	z	z	PROPN
ma-136	619	49	∈	∈	PROPN
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ma-136	619	53	(	(	PUNCT
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ma-136	619	55	)	)	PUNCT
ma-136	619	56	,	,	PUNCT
ma-136	619	57	we	we	PRON
ma-136	619	58	obtain	obtain	VERB
ma-136	619	59	t	t	NOUN
ma-136	619	60	(	(	PUNCT
ma-136	619	61	r	r	NOUN
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ma-136	619	64	)	)	PUNCT
ma-136	619	65	t	t	NOUN
ma-136	619	66	(	(	PUNCT
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ma-136	619	71	≤	≤	PROPN
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ma-136	619	73	(	(	PUNCT
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ma-136	619	75	,	,	PUNCT
ma-136	619	76	z	z	NOUN
ma-136	619	77	)	)	PUNCT
ma-136	619	78	expp−1	expp−1	NOUN
ma-136	619	79	{	{	PUNCT
ma-136	619	80	γ	γ	X
ma-136	619	81	(	(	PUNCT
ma-136	619	82	logq−1	logq−1	X
ma-136	619	83	(	(	PUNCT
ma-136	619	84	1	1	NUM
ma-136	619	85	1−|z	1−|z	NUM
ma-136	619	86	|	|	NOUN
ma-136	619	87	)	)	PUNCT
ma-136	619	88	)	)	PUNCT
ma-136	619	89	µ	µ	X
ma-136	619	90	}	}	PUNCT
ma-136	619	91	→	→	SYM
ma-136	619	92	0	0	NUM
ma-136	619	93	(	(	PUNCT
ma-136	619	94	5.4	5.4	NUM
ma-136	619	95	)	)	PUNCT
ma-136	619	96	as	as	ADP
ma-136	619	97	|z	|z	PROPN
ma-136	619	98	|	|	PROPN
ma-136	619	99	→	→	SYM
ma-136	619	100	1−	1−	NUM
ma-136	619	101	for	for	ADP
ma-136	619	102	z	z	PROPN
ma-136	619	103	∈	∈	PROPN
ma-136	619	104	h.	h.	NOUN
ma-136	619	105	then	then	ADV
ma-136	619	106	,	,	PUNCT
ma-136	619	107	by	by	ADP
ma-136	619	108	(	(	PUNCT
ma-136	619	109	5.2	5.2	NUM
ma-136	619	110	)	)	PUNCT
ma-136	619	111	and	and	CCONJ
ma-136	619	112	(	(	PUNCT
ma-136	619	113	5.4	5.4	NUM
ma-136	619	114	)	)	PUNCT
ma-136	619	115	,	,	PUNCT
ma-136	619	116	we	we	PRON
ma-136	619	117	get	get	VERB
ma-136	619	118	lim	lim	PROPN
ma-136	619	119	|z	|z	PROPN
ma-136	619	120	|→1−,z∈h	|→1−,z∈h	PROPN
ma-136	620	1	t	t	PROPN
ma-136	620	2	(	(	PUNCT
ma-136	620	3	r	r	NOUN
ma-136	620	4	,	,	PUNCT
ma-136	620	5	a1	a1	NOUN
ma-136	620	6	)	)	PUNCT
ma-136	620	7	t	t	NOUN
ma-136	620	8	(	(	PUNCT
ma-136	620	9	r	r	NOUN
ma-136	620	10	,	,	PUNCT
ma-136	620	11	a0	a0	NOUN
ma-136	620	12	)	)	PUNCT
ma-136	620	13	=	=	SYM
ma-136	620	14	1	1	X
ma-136	620	15	.	.	PUNCT
ma-136	620	16	(	(	PUNCT
ma-136	620	17	5.5	5.5	NUM
ma-136	620	18	)	)	PUNCT
ma-136	620	19	on	on	ADP
ma-136	620	20	the	the	DET
ma-136	620	21	other	other	ADJ
ma-136	620	22	hand	hand	NOUN
ma-136	620	23	,	,	PUNCT
ma-136	620	24	we	we	PRON
ma-136	620	25	have	have	VERB
ma-136	620	26	for	for	ADP
ma-136	620	27	p	p	NOUN
ma-136	620	28	=	=	NOUN
ma-136	620	29	q	q	NOUN
ma-136	620	30	=	=	SYM
ma-136	620	31	1	1	NUM
ma-136	620	32	t	t	NOUN
ma-136	620	33	(	(	PUNCT
ma-136	620	34	r	r	NOUN
ma-136	620	35	,	,	PUNCT
ma-136	620	36	a1	a1	NOUN
ma-136	620	37	)	)	PUNCT
ma-136	620	38	t	t	NOUN
ma-136	620	39	(	(	PUNCT
ma-136	620	40	r	r	NOUN
ma-136	620	41	,	,	PUNCT
ma-136	620	42	a0	a0	PROPN
ma-136	620	43	)	)	PUNCT
ma-136	620	44	<	<	X
ma-136	621	1	α	α	X
ma-136	621	2	γ	γ	X
ma-136	621	3	<	<	X
ma-136	621	4	1	1	NUM
ma-136	621	5	(	(	PUNCT
ma-136	621	6	5.6	5.6	NUM
ma-136	621	7	)	)	PUNCT
ma-136	621	8	and	and	CCONJ
ma-136	621	9	for	for	ADP
ma-136	621	10	p	p	PROPN
ma-136	621	11	≥	≥	NOUN
ma-136	621	12	q	q	X
ma-136	621	13	≥	≥	NUM
ma-136	621	14	2	2	NUM
ma-136	621	15	t	t	NOUN
ma-136	621	16	(	(	PUNCT
ma-136	621	17	r	r	NOUN
ma-136	621	18	,	,	PUNCT
ma-136	621	19	a1	a1	NOUN
ma-136	621	20	)	)	PUNCT
ma-136	621	21	t	t	NOUN
ma-136	621	22	(	(	PUNCT
ma-136	621	23	r	r	NOUN
ma-136	621	24	,	,	PUNCT
ma-136	621	25	a0	a0	NOUN
ma-136	621	26	)	)	PUNCT
ma-136	621	27	<	<	X
ma-136	621	28	expp−1	expp−1	PROPN
ma-136	621	29	{	{	PUNCT
ma-136	621	30	α	α	PROPN
ma-136	621	31	(	(	PUNCT
ma-136	621	32	logq−1	logq−1	X
ma-136	621	33	(	(	PUNCT
ma-136	621	34	1	1	NUM
ma-136	621	35	1−|z	1−|z	NUM
ma-136	621	36	|	|	NOUN
ma-136	621	37	)	)	PUNCT
ma-136	621	38	)	)	PUNCT
ma-136	621	39	µ	µ	X
ma-136	621	40	}	}	PUNCT
ma-136	621	41	expp−1	expp−1	PROPN
ma-136	621	42	{	{	PUNCT
ma-136	621	43	γ	γ	X
ma-136	621	44	(	(	PUNCT
ma-136	621	45	logq−1	logq−1	X
ma-136	621	46	(	(	PUNCT
ma-136	621	47	1	1	NUM
ma-136	621	48	1−|z	1−|z	NUM
ma-136	621	49	|	|	NOUN
ma-136	621	50	)	)	PUNCT
ma-136	621	51	)	)	PUNCT
ma-136	621	52	µ	µ	X
ma-136	621	53	}	}	PUNCT
ma-136	621	54	→	→	SYM
ma-136	621	55	0	0	NUM
ma-136	621	56	(	(	PUNCT
ma-136	621	57	5.7	5.7	NUM
ma-136	621	58	)	)	PUNCT
ma-136	621	59	as	as	ADP
ma-136	621	60	|z	|z	PROPN
ma-136	621	61	|	|	PROPN
ma-136	621	62	→	→	SYM
ma-136	621	63	1−	1−	NUM
ma-136	621	64	for	for	ADP
ma-136	621	65	z	z	PROPN
ma-136	621	66	∈	∈	PROPN
ma-136	621	67	h.	h.	NOUN
ma-136	622	1	it	it	PRON
ma-136	622	2	follows	follow	VERB
ma-136	622	3	by	by	ADP
ma-136	622	4	(	(	PUNCT
ma-136	622	5	5.6	5.6	NUM
ma-136	622	6	)	)	PUNCT
ma-136	622	7	and	and	CCONJ
ma-136	622	8	(	(	PUNCT
ma-136	622	9	5.7	5.7	NUM
ma-136	622	10	)	)	PUNCT
ma-136	623	1	that	that	SCONJ
ma-136	623	2	lim	lim	PROPN
ma-136	623	3	|z	|z	PROPN
ma-136	623	4	|→1−,z∈h	|→1−,z∈h	PROPN
ma-136	624	1	t	t	PROPN
ma-136	625	1	(	(	PUNCT
ma-136	625	2	r	r	NOUN
ma-136	625	3	,	,	PUNCT
ma-136	625	4	a1	a1	NOUN
ma-136	625	5	)	)	PUNCT
ma-136	625	6	t	t	NOUN
ma-136	625	7	(	(	PUNCT
ma-136	625	8	r	r	NOUN
ma-136	625	9	,	,	PUNCT
ma-136	625	10	a0	a0	PROPN
ma-136	625	11	)	)	PUNCT
ma-136	625	12	6=	6=	ADP
ma-136	625	13	1	1	X
ma-136	625	14	.	.	PUNCT
ma-136	625	15	(	(	PUNCT
ma-136	625	16	5.8	5.8	NUM
ma-136	625	17	)	)	PUNCT
ma-136	625	18	obviously	obviously	ADV
ma-136	625	19	,	,	PUNCT
ma-136	625	20	(	(	PUNCT
ma-136	625	21	5.5	5.5	NUM
ma-136	625	22	)	)	PUNCT
ma-136	625	23	contradicts	contradict	VERB
ma-136	625	24	with	with	ADP
ma-136	625	25	(	(	PUNCT
ma-136	625	26	5.8	5.8	NUM
ma-136	625	27	)	)	PUNCT
ma-136	625	28	.	.	PUNCT
ma-136	626	1	hence	hence	ADV
ma-136	626	2	,	,	PUNCT
ma-136	626	3	−a1	−a1	VERB
ma-136	626	4	−	−	PROPN
ma-136	626	5	za0	za0	NOUN
ma-136	626	6	6≡	6≡	NUM
ma-136	626	7	0	0	X
ma-136	626	8	.	.	PUNCT
ma-136	627	1	set	set	VERB
ma-136	627	2	ak	ak	PROPN
ma-136	627	3	(	(	PUNCT
ma-136	627	4	z	z	NOUN
ma-136	627	5	)	)	PUNCT
ma-136	627	6	≡	≡	PROPN
ma-136	627	7	1	1	NUM
ma-136	627	8	,	,	PUNCT
ma-136	627	9	then	then	ADV
ma-136	627	10	t	t	PROPN
ma-136	627	11	(	(	PUNCT
ma-136	627	12	r	r	PROPN
ma-136	627	13	,	,	PUNCT
ma-136	627	14	ak	ak	NOUN
ma-136	627	15	)	)	PUNCT
ma-136	627	16	≤	≤	NOUN
ma-136	627	17	expp−1	expp−1	PROPN
ma-136	627	18	{	{	PUNCT
ma-136	627	19	α	α	PROPN
ma-136	627	20	(	(	PUNCT
ma-136	627	21	logq−1	logq−1	X
ma-136	627	22	(	(	PUNCT
ma-136	627	23	1	1	NUM
ma-136	627	24	1−|z	1−|z	NUM
ma-136	627	25	|	|	NOUN
ma-136	627	26	)	)	PUNCT
ma-136	627	27	)	)	PUNCT
ma-136	627	28	µ	µ	X
ma-136	627	29	}	}	PUNCT
ma-136	627	30	.	.	PUNCT
ma-136	628	1	clearly	clearly	ADV
ma-136	628	2	,	,	PUNCT
ma-136	628	3	a0	a0	PROPN
ma-136	628	4	6≡	6≡	NUM
ma-136	628	5	0	0	NUM
ma-136	628	6	.	.	PUNCT
ma-136	629	1	we	we	PRON
ma-136	629	2	can	can	AUX
ma-136	629	3	get	get	VERB
ma-136	629	4	the	the	DET
ma-136	629	5	conclusion	conclusion	NOUN
ma-136	629	6	of	of	ADP
ma-136	629	7	theorem	theorem	NOUN
ma-136	629	8	1.10	1.10	NUM
ma-136	629	9	,	,	PUNCT
ma-136	629	10	byreasoning	byreasoning	NOUN
ma-136	629	11	in	in	ADP
ma-136	629	12	the	the	DET
ma-136	629	13	same	same	ADJ
ma-136	629	14	way	way	NOUN
ma-136	629	15	as	as	SCONJ
ma-136	629	16	we	we	PRON
ma-136	629	17	did	do	VERB
ma-136	629	18	in	in	ADP
ma-136	629	19	the	the	DET
ma-136	629	20	proof	proof	NOUN
ma-136	629	21	of	of	ADP
ma-136	629	22	theorem	theorem	NOUN
ma-136	629	23	1.9	1.9	NUM
ma-136	629	24	.	.	PUNCT
ma-136	630	1	proof	proof	NOUN
ma-136	630	2	of	of	ADP
ma-136	630	3	theorem	theorem	ADJ
ma-136	630	4	1.11	1.11	NUM
ma-136	630	5	.	.	PUNCT
ma-136	630	6	suppose	suppose	VERB
ma-136	630	7	that	that	SCONJ
ma-136	630	8	every	every	DET
ma-136	630	9	meromorphic	meromorphic	ADJ
ma-136	630	10	(	(	PUNCT
ma-136	630	11	or	or	CCONJ
ma-136	630	12	analytic	analytic	ADJ
ma-136	630	13	)	)	PUNCT
ma-136	630	14	solution	solution	NOUN
ma-136	630	15	f	f	PROPN
ma-136	630	16	of	of	ADP
ma-136	630	17	equation	equation	NOUN
ma-136	630	18	(	(	PUNCT
ma-136	630	19	1.2)not	1.2)not	NUM
ma-136	630	20	being	be	AUX
ma-136	630	21	identically	identically	ADV
ma-136	630	22	equal	equal	ADJ
ma-136	630	23	to	to	ADP
ma-136	630	24	0	0	NUM
ma-136	630	25	.	.	PUNCT
ma-136	630	26	by	by	ADP
ma-136	630	27	applying	apply	VERB
ma-136	630	28	one	one	NUM
ma-136	630	29	of	of	ADP
ma-136	630	30	theorem	theorem	ADJ
ma-136	630	31	1.5	1.5	NUM
ma-136	630	32	to	to	PART
ma-136	630	33	theorem	theorem	VERB
ma-136	630	34	1.8	1.8	NUM
ma-136	630	35	,	,	PUNCT
ma-136	630	36	we	we	PRON
ma-136	630	37	get	get	VERB
ma-136	630	38	σ[p	σ[p	NOUN
ma-136	630	39	,	,	PUNCT
ma-136	630	40	q	q	X
ma-136	630	41	]	]	X
ma-136	630	42	(	(	PUNCT
ma-136	630	43	f	f	X
ma-136	630	44	)	)	PUNCT
ma-136	630	45	=	=	NOUN
ma-136	630	46	∞	∞	NOUN
ma-136	630	47	,	,	PUNCT
ma-136	630	48	σ[p+1,q	σ[p+1,q	NOUN
ma-136	630	49	]	]	PUNCT
ma-136	630	50	(	(	PUNCT
ma-136	630	51	f	f	PROPN
ma-136	630	52	)	)	PUNCT
ma-136	630	53	≥	≥	PROPN
ma-136	630	54	µ.	µ.	NOUN
ma-136	630	55	then	then	ADV
ma-136	630	56	,	,	PUNCT
ma-136	630	57	we	we	PRON
ma-136	630	58	can	can	AUX
ma-136	630	59	get	get	VERB
ma-136	630	60	the	the	DET
ma-136	630	61	conclusion	conclusion	NOUN
ma-136	630	62	of	of	ADP
ma-136	630	63	theorem	theorem	NOUN
ma-136	630	64	1.11	1.11	NUM
ma-136	630	65	,	,	PUNCT
ma-136	630	66	by	by	ADP
ma-136	630	67	reasoning	reason	VERB
ma-136	630	68	in	in	ADP
ma-136	630	69	the	the	DET
ma-136	630	70	same	same	ADJ
ma-136	630	71	way	way	NOUN
ma-136	630	72	as	as	SCONJ
ma-136	630	73	we	we	PRON
ma-136	630	74	did	do	VERB
ma-136	630	75	in	in	ADP
ma-136	630	76	theproof	theproof	NOUN
ma-136	630	77	of	of	ADP
ma-136	630	78	theorem	theorem	ADJ
ma-136	630	79	1.9	1.9	NUM
ma-136	630	80	and	and	CCONJ
ma-136	630	81	theorem	theorem	VERB
ma-136	630	82	1.10	1.10	NUM
ma-136	630	83	by	by	ADP
ma-136	630	84	using	use	VERB
ma-136	630	85	σ[p+1,q	σ[p+1,q	NOUN
ma-136	630	86	]	]	PUNCT
ma-136	630	87	(	(	PUNCT
ma-136	630	88	f	f	PROPN
ma-136	630	89	)	)	PUNCT
ma-136	630	90	≥	≥	PROPN
ma-136	630	91	µ	µ	X
ma-136	630	92	instead	instead	ADV
ma-136	630	93	of	of	ADP
ma-136	630	94	σ[p+1,q	σ[p+1,q	NOUN
ma-136	630	95	]	]	PUNCT
ma-136	630	96	(	(	PUNCT
ma-136	630	97	f	f	X
ma-136	630	98	)	)	PUNCT
ma-136	631	1	=	=	SYM
ma-136	631	2	µ	µ	X
ma-136	631	3	and	and	CCONJ
ma-136	631	4	σ[p+1,q	σ[p+1,q	NOUN
ma-136	631	5	]	]	PUNCT
ma-136	631	6	(	(	PUNCT
ma-136	631	7	f	f	X
ma-136	631	8	(	(	PUNCT
ma-136	631	9	j	j	PROPN
ma-136	631	10	)	)	PUNCT
ma-136	631	11	)	)	PUNCT
ma-136	631	12	≥	≥	PROPN
ma-136	631	13	µ	µ	X
ma-136	631	14	instead	instead	ADV
ma-136	631	15	of	of	ADP
ma-136	631	16	σ[p+1,q	σ[p+1,q	NOUN
ma-136	631	17	]	]	PUNCT
ma-136	631	18	(	(	PUNCT
ma-136	631	19	f	f	X
ma-136	631	20	(	(	PUNCT
ma-136	631	21	j	j	NOUN
ma-136	631	22	)	)	PUNCT
ma-136	631	23	)	)	PUNCT
ma-136	632	1	=	=	SYM
ma-136	632	2	µ	µ	X
ma-136	632	3	(	(	PUNCT
ma-136	632	4	j	j	NOUN
ma-136	632	5	=	=	SYM
ma-136	632	6	1	1	NUM
ma-136	632	7	,	,	PUNCT
ma-136	632	8	2	2	NUM
ma-136	632	9	,	,	PUNCT
ma-136	632	10	...	...	PUNCT
ma-136	632	11	)	)	PUNCT
ma-136	632	12	.	.	PUNCT
ma-136	633	1	https://doi.org/10.28924/ada/ma.3.10	https://doi.org/10.28924/ada/ma.3.10	ADV
ma-136	633	2	eur	eur	PROPN
ma-136	633	3	.	.	PUNCT
ma-136	634	1	j.	j.	PROPN
ma-136	634	2	math	math	PROPN
ma-136	634	3	.	.	PUNCT
ma-136	635	1	anal	anal	PROPN
ma-136	635	2	.	.	PUNCT
ma-136	636	1	10.28924	10.28924	NUM
ma-136	636	2	/	/	SYM
ma-136	636	3	ada	ada	NOUN
ma-136	636	4	/	/	NOUN
ma-136	636	5	ma.3.10	ma.3.10	ADJ
ma-136	636	6	246	246	NUM
ma-136	636	7	.	.	PUNCT
ma-136	637	1	examples	example	NOUN
ma-136	637	2	example	example	NOUN
ma-136	637	3	6.1	6.1	NUM
ma-136	637	4	consider	consider	VERB
ma-136	637	5	the	the	DET
ma-136	637	6	following	follow	VERB
ma-136	637	7	differential	differential	ADJ
ma-136	637	8	equation	equation	NOUN
ma-136	638	1	f	f	PROPN
ma-136	638	2	′′	′′	PROPN
ma-136	638	3	+	+	PROPN
ma-136	638	4	k1	k1	PROPN
ma-136	638	5	(	(	PUNCT
ma-136	638	6	z	z	NOUN
ma-136	638	7	)	)	PUNCT
ma-136	638	8	exp4	exp4	NOUN
ma-136	638	9	{	{	PUNCT
ma-136	638	10	(	(	PUNCT
ma-136	638	11	log2	log2	PROPN
ma-136	638	12	(	(	PUNCT
ma-136	638	13	1	1	NUM
ma-136	638	14	1−	1−	NUM
ma-136	638	15	z	z	NOUN
ma-136	638	16	)	)	PUNCT
ma-136	638	17	)	)	PUNCT
ma-136	638	18	5	5	X
ma-136	638	19	}	}	PUNCT
ma-136	638	20	f	f	NOUN
ma-136	638	21	′	′	NUM
ma-136	639	1	+	+	PROPN
ma-136	639	2	k0	k0	PROPN
ma-136	639	3	(	(	PUNCT
ma-136	639	4	z	z	NOUN
ma-136	639	5	)	)	PUNCT
ma-136	639	6	exp4	exp4	NOUN
ma-136	639	7	{	{	PUNCT
ma-136	639	8	3	3	NUM
ma-136	639	9	(	(	PUNCT
ma-136	639	10	log2	log2	PROPN
ma-136	639	11	(	(	PUNCT
ma-136	639	12	1	1	NUM
ma-136	639	13	1−	1−	NUM
ma-136	639	14	z	z	NOUN
ma-136	639	15	)	)	PUNCT
ma-136	639	16	)	)	PUNCT
ma-136	639	17	5	5	X
ma-136	639	18	}	}	PUNCT
ma-136	639	19	f	f	NOUN
ma-136	639	20	=	=	SYM
ma-136	639	21	0	0	NUM
ma-136	639	22	,	,	PUNCT
ma-136	639	23	(	(	PUNCT
ma-136	639	24	6.1	6.1	NUM
ma-136	639	25	)	)	PUNCT
ma-136	639	26	where	where	SCONJ
ma-136	639	27	k0	k0	PROPN
ma-136	639	28	and	and	CCONJ
ma-136	639	29	k1	k1	PROPN
ma-136	639	30	are	be	AUX
ma-136	639	31	analytic	analytic	ADJ
ma-136	639	32	functions	function	NOUN
ma-136	639	33	in	in	ADP
ma-136	639	34	the	the	DET
ma-136	639	35	unit	unit	NOUN
ma-136	639	36	disc	disc	VERB
ma-136	639	37	d	d	PROPN
ma-136	639	38	such	such	ADJ
ma-136	639	39	that	that	DET
ma-136	639	40	|k0|	|k0|	NOUN
ma-136	639	41	>	>	X
ma-136	639	42	1	1	NUM
ma-136	639	43	,	,	PUNCT
ma-136	639	44	|k1|	|k1|	NOUN
ma-136	639	45	<	<	X
ma-136	639	46	1	1	NUM
ma-136	639	47	and	and	CCONJ
ma-136	639	48	max	max	PROPN
ma-136	639	49	{	{	PUNCT
ma-136	639	50	σm,[4,3	σm,[4,3	PROPN
ma-136	639	51	]	]	X
ma-136	639	52	(	(	PUNCT
ma-136	639	53	k0	k0	PROPN
ma-136	639	54	)	)	PUNCT
ma-136	639	55	,	,	PUNCT
ma-136	639	56	σm,[4,3	σm,[4,3	PROPN
ma-136	639	57	]	]	X
ma-136	639	58	(	(	PUNCT
ma-136	639	59	k1	k1	NOUN
ma-136	639	60	)	)	PUNCT
ma-136	639	61	}	}	PUNCT
ma-136	639	62	<	<	X
ma-136	639	63	5	5	X
ma-136	639	64	.	.	PUNCT
ma-136	640	1	in	in	ADP
ma-136	640	2	the	the	DET
ma-136	640	3	equation	equation	NOUN
ma-136	640	4	(	(	PUNCT
ma-136	640	5	6.1	6.1	NUM
ma-136	640	6	)	)	PUNCT
ma-136	640	7	,	,	PUNCT
ma-136	640	8	we	we	PRON
ma-136	640	9	have	have	VERB
ma-136	640	10	a0	a0	NOUN
ma-136	640	11	(	(	PUNCT
ma-136	640	12	z	z	NOUN
ma-136	640	13	)	)	PUNCT
ma-136	640	14	=	=	SYM
ma-136	640	15	k0	k0	PROPN
ma-136	640	16	(	(	PUNCT
ma-136	640	17	z	z	NOUN
ma-136	640	18	)	)	PUNCT
ma-136	640	19	exp4	exp4	NOUN
ma-136	640	20	{	{	PUNCT
ma-136	640	21	3	3	NUM
ma-136	640	22	(	(	PUNCT
ma-136	640	23	log2	log2	PROPN
ma-136	640	24	(	(	PUNCT
ma-136	640	25	1	1	NUM
ma-136	640	26	1−	1−	NUM
ma-136	640	27	z	z	NOUN
ma-136	640	28	)	)	PUNCT
ma-136	640	29	)	)	PUNCT
ma-136	640	30	5	5	X
ma-136	640	31	}	}	PUNCT
ma-136	640	32	,	,	PUNCT
ma-136	640	33	a1	a1	NOUN
ma-136	640	34	(	(	PUNCT
ma-136	640	35	z	z	NOUN
ma-136	640	36	)	)	PUNCT
ma-136	640	37	=	=	SYM
ma-136	640	38	k1	k1	X
ma-136	640	39	(	(	PUNCT
ma-136	640	40	z	z	NOUN
ma-136	640	41	)	)	PUNCT
ma-136	640	42	exp4	exp4	NOUN
ma-136	640	43	{	{	PUNCT
ma-136	640	44	(	(	PUNCT
ma-136	640	45	log2	log2	PROPN
ma-136	640	46	(	(	PUNCT
ma-136	640	47	1	1	NUM
ma-136	640	48	1−	1−	NUM
ma-136	640	49	z	z	NOUN
ma-136	640	50	)	)	PUNCT
ma-136	640	51	)	)	PUNCT
ma-136	640	52	5	5	NUM
ma-136	640	53	}	}	PUNCT
ma-136	640	54	.	.	PUNCT
ma-136	641	1	then	then	ADV
ma-136	641	2	max	max	PROPN
ma-136	641	3	{	{	PUNCT
ma-136	641	4	σm,[4,3	σm,[4,3	PROPN
ma-136	641	5	]	]	X
ma-136	641	6	(	(	PUNCT
ma-136	641	7	a0	a0	PROPN
ma-136	641	8	)	)	PUNCT
ma-136	641	9	,	,	PUNCT
ma-136	641	10	σm,[4,3	σm,[4,3	PROPN
ma-136	641	11	]	]	X
ma-136	641	12	(	(	PUNCT
ma-136	641	13	a1	a1	NOUN
ma-136	641	14	)	)	PUNCT
ma-136	641	15	}	}	PUNCT
ma-136	642	1	=	=	PUNCT
ma-136	642	2	5.let	5.let	NUM
ma-136	642	3	h	h	NOUN
ma-136	642	4	=	=	PRON
ma-136	642	5	{	{	PUNCT
ma-136	642	6	z	z	NOUN
ma-136	642	7	∈	∈	PROPN
ma-136	642	8	c	c	NOUN
ma-136	642	9	:	:	PUNCT
ma-136	642	10	|z	|z	PROPN
ma-136	643	1	|	|	ADV
ma-136	643	2	=	=	SYM
ma-136	643	3	r	r	NOUN
ma-136	643	4	<	<	X
ma-136	643	5	1	1	NUM
ma-136	643	6	and	and	CCONJ
ma-136	643	7	arg	arg	NOUN
ma-136	643	8	z	z	NOUN
ma-136	643	9	=	=	SYM
ma-136	643	10	0	0	NUM
ma-136	643	11	}	}	PUNCT
ma-136	643	12	⊂	⊂	PROPN
ma-136	644	1	d	d	AUX
ma-136	644	2	be	be	AUX
ma-136	644	3	a	a	DET
ma-136	644	4	set	set	NOUN
ma-136	644	5	of	of	ADP
ma-136	644	6	complex	complex	ADJ
ma-136	644	7	numbers	number	NOUN
ma-136	644	8	satisfying	satisfy	VERB
ma-136	644	9	densd	densd	PROPN
ma-136	644	10	{	{	PUNCT
ma-136	644	11	|z	|z	PROPN
ma-136	645	1	|	|	ADV
ma-136	645	2	:	:	PUNCT
ma-136	645	3	z	z	PROPN
ma-136	645	4	∈	∈	PROPN
ma-136	646	1	h	h	NOUN
ma-136	646	2	}	}	PUNCT
ma-136	646	3	=	=	SYM
ma-136	646	4	1	1	NUM
ma-136	646	5	>	>	X
ma-136	646	6	0	0	X
ma-136	646	7	.	.	PUNCT
ma-136	647	1	then	then	ADV
ma-136	647	2	|a0	|a0	PROPN
ma-136	647	3	(	(	PUNCT
ma-136	647	4	z)|	z)|	NOUN
ma-136	647	5	=	=	SYM
ma-136	647	6	|k0	|k0	NOUN
ma-136	647	7	(	(	PUNCT
ma-136	647	8	z)|	z)|	X
ma-136	647	9	∣∣∣∣∣exp4	∣∣∣∣∣exp4	PROPN
ma-136	647	10	{	{	PUNCT
ma-136	647	11	3	3	NUM
ma-136	647	12	(	(	PUNCT
ma-136	647	13	log2	log2	PROPN
ma-136	647	14	(	(	PUNCT
ma-136	647	15	1	1	NUM
ma-136	647	16	1−	1−	NUM
ma-136	647	17	z	z	NOUN
ma-136	647	18	)	)	PUNCT
ma-136	647	19	)	)	PUNCT
ma-136	647	20	5}∣∣∣∣∣	5}∣∣∣∣∣	PROPN
ma-136	647	21	>	>	X
ma-136	647	22	exp4	exp4	NOUN
ma-136	647	23	{	{	PUNCT
ma-136	647	24	3	3	NUM
ma-136	647	25	(	(	PUNCT
ma-136	647	26	log2	log2	PROPN
ma-136	647	27	(	(	PUNCT
ma-136	647	28	1	1	NUM
ma-136	647	29	1−	1−	NUM
ma-136	647	30	r	r	NOUN
ma-136	647	31	)	)	PUNCT
ma-136	647	32	)	)	PUNCT
ma-136	647	33	5	5	X
ma-136	647	34	}	}	PUNCT
ma-136	647	35	⇒	⇒	VERB
ma-136	647	36	log4	log4	NOUN
ma-136	647	37	|a0	|a0	PROPN
ma-136	647	38	(	(	PUNCT
ma-136	647	39	z)|	z)|	X
ma-136	647	40	(	(	PUNCT
ma-136	647	41	log2	log2	PROPN
ma-136	647	42	(	(	PUNCT
ma-136	647	43	1	1	NUM
ma-136	647	44	1−r	1−r	NUM
ma-136	647	45	)	)	PUNCT
ma-136	647	46	)	)	PUNCT
ma-136	647	47	5	5	X
ma-136	647	48	>	>	SYM
ma-136	647	49	3⇒	3⇒	NUM
ma-136	647	50	lim	lim	PROPN
ma-136	647	51	inf	inf	PROPN
ma-136	647	52	r→1−,z∈h	r→1−,z∈h	PROPN
ma-136	647	53	log4	log4	PROPN
ma-136	647	54	|a0	|a0	PROPN
ma-136	648	1	(	(	PUNCT
ma-136	648	2	z)|	z)|	X
ma-136	648	3	(	(	PUNCT
ma-136	648	4	log2	log2	PROPN
ma-136	648	5	(	(	PUNCT
ma-136	648	6	1	1	NUM
ma-136	648	7	1−r	1−r	NUM
ma-136	648	8	)	)	PUNCT
ma-136	648	9	)	)	PUNCT
ma-136	648	10	5	5	NUM
ma-136	648	11	≥	≥	NOUN
ma-136	648	12	3	3	NUM
ma-136	648	13	>	>	SYM
ma-136	648	14	1	1	NUM
ma-136	648	15	,	,	PUNCT
ma-136	648	16	and	and	CCONJ
ma-136	648	17	|a1	|a1	NOUN
ma-136	648	18	(	(	PUNCT
ma-136	648	19	z)|	z)|	NOUN
ma-136	648	20	=	=	SYM
ma-136	648	21	|k1	|k1	NOUN
ma-136	648	22	(	(	PUNCT
ma-136	648	23	z)|	z)|	X
ma-136	648	24	∣∣∣∣∣exp4	∣∣∣∣∣exp4	PROPN
ma-136	648	25	{	{	PUNCT
ma-136	648	26	(	(	PUNCT
ma-136	648	27	log2	log2	PROPN
ma-136	648	28	(	(	PUNCT
ma-136	648	29	1	1	NUM
ma-136	648	30	1−	1−	NUM
ma-136	648	31	z	z	NOUN
ma-136	648	32	)	)	PUNCT
ma-136	648	33	)	)	PUNCT
ma-136	648	34	5}∣∣∣∣∣	5}∣∣∣∣∣	PROPN
ma-136	648	35	≤	≤	PROPN
ma-136	648	36	exp4	exp4	NOUN
ma-136	648	37	{	{	PUNCT
ma-136	648	38	(	(	PUNCT
ma-136	648	39	log2	log2	PROPN
ma-136	648	40	(	(	PUNCT
ma-136	648	41	1	1	NUM
ma-136	648	42	1−	1−	NUM
ma-136	648	43	r	r	NOUN
ma-136	648	44	)	)	PUNCT
ma-136	648	45	)	)	PUNCT
ma-136	648	46	5	5	X
ma-136	648	47	}	}	PUNCT
ma-136	648	48	as	as	ADP
ma-136	648	49	r	r	NOUN
ma-136	648	50	→	→	SYM
ma-136	648	51	1−	1−	NUM
ma-136	648	52	for	for	ADP
ma-136	648	53	z	z	PROPN
ma-136	648	54	∈	∈	PROPN
ma-136	648	55	h.	h.	NOUN
ma-136	648	56	it	it	PRON
ma-136	648	57	is	be	AUX
ma-136	648	58	clear	clear	ADJ
ma-136	648	59	that	that	SCONJ
ma-136	648	60	the	the	DET
ma-136	648	61	conditions	condition	NOUN
ma-136	648	62	of	of	ADP
ma-136	648	63	theorem	theorem	ADJ
ma-136	648	64	1.1	1.1	NUM
ma-136	648	65	hold	hold	NOUN
ma-136	648	66	with	with	ADP
ma-136	648	67	α	α	NOUN
ma-136	648	68	=	=	SYM
ma-136	648	69	1	1	NUM
ma-136	648	70	,	,	PUNCT
ma-136	648	71	µ	µ	X
ma-136	648	72	=	=	SYM
ma-136	648	73	5	5	NUM
ma-136	648	74	,	,	PUNCT
ma-136	648	75	p	p	NOUN
ma-136	648	76	=	=	PUNCT
ma-136	648	77	4and	4and	NUM
ma-136	648	78	q	q	NOUN
ma-136	648	79	=	=	SYM
ma-136	648	80	3	3	NUM
ma-136	648	81	on	on	ADP
ma-136	648	82	the	the	DET
ma-136	648	83	set	set	NOUN
ma-136	648	84	h.	h.	PROPN
ma-136	648	85	by	by	ADP
ma-136	648	86	theorem	theorem	ADJ
ma-136	648	87	1.1	1.1	NUM
ma-136	648	88	,	,	PUNCT
ma-136	648	89	every	every	DET
ma-136	648	90	solution	solution	NOUN
ma-136	648	91	f	f	PROPN
ma-136	648	92	6≡	6≡	NUM
ma-136	648	93	0	0	NUM
ma-136	648	94	of	of	ADP
ma-136	648	95	equation	equation	NOUN
ma-136	648	96	(	(	PUNCT
ma-136	648	97	6.1	6.1	NUM
ma-136	648	98	)	)	PUNCT
ma-136	648	99	satisfies	satisfie	NOUN
ma-136	648	100	σ[4,3	σ[4,3	NOUN
ma-136	648	101	]	]	PUNCT
ma-136	648	102	(	(	PUNCT
ma-136	648	103	f	f	X
ma-136	648	104	)	)	PUNCT
ma-136	649	1	=	=	SYM
ma-136	649	2	σm,[4,3	σm,[4,3	PROPN
ma-136	649	3	]	]	X
ma-136	649	4	(	(	PUNCT
ma-136	649	5	f	f	X
ma-136	649	6	)	)	PUNCT
ma-136	650	1	=	=	NOUN
ma-136	650	2	∞	∞	PROPN
ma-136	650	3	and	and	CCONJ
ma-136	650	4	σ[5,3	σ[5,3	NOUN
ma-136	650	5	]	]	PUNCT
ma-136	650	6	(	(	PUNCT
ma-136	650	7	f	f	X
ma-136	650	8	)	)	PUNCT
ma-136	650	9	=	=	SYM
ma-136	651	1	σm,[5,3	σm,[5,3	PROPN
ma-136	651	2	]	]	PUNCT
ma-136	651	3	(	(	PUNCT
ma-136	651	4	f	f	X
ma-136	651	5	)	)	PUNCT
ma-136	651	6	=	=	SYM
ma-136	652	1	σm,[5,3	σm,[5,3	PROPN
ma-136	652	2	]	]	X
ma-136	652	3	(	(	PUNCT
ma-136	652	4	a0	a0	PROPN
ma-136	652	5	)	)	PUNCT
ma-136	652	6	=	=	SYM
ma-136	653	1	5	5	X
ma-136	653	2	.	.	X
ma-136	653	3	https://doi.org/10.28924/ada/ma.3.10	https://doi.org/10.28924/ada/ma.3.10	PROPN
ma-136	653	4	eur	eur	PROPN
ma-136	653	5	.	.	PUNCT
ma-136	654	1	j.	j.	PROPN
ma-136	654	2	math	math	PROPN
ma-136	654	3	.	.	PUNCT
ma-136	655	1	anal	anal	PROPN
ma-136	655	2	.	.	PUNCT
ma-136	656	1	10.28924	10.28924	NUM
ma-136	656	2	/	/	SYM
ma-136	656	3	ada	ada	NOUN
ma-136	656	4	/	/	SYM
ma-136	656	5	ma.3.10	ma.3.10	ADJ
ma-136	656	6	25	25	NUM
ma-136	656	7	example	example	NOUN
ma-136	656	8	6.2	6.2	NUM
ma-136	656	9	consider	consider	VERB
ma-136	656	10	the	the	DET
ma-136	656	11	following	follow	VERB
ma-136	656	12	differential	differential	ADJ
ma-136	656	13	equation	equation	NOUN
ma-136	656	14	k2	k2	NOUN
ma-136	656	15	(	(	PUNCT
ma-136	656	16	z	z	NOUN
ma-136	656	17	)	)	PUNCT
ma-136	656	18	exp4	exp4	NOUN
ma-136	656	19	{	{	PUNCT
ma-136	656	20	(	(	PUNCT
ma-136	656	21	log2	log2	PROPN
ma-136	656	22	(	(	PUNCT
ma-136	656	23	1	1	NUM
ma-136	656	24	1−z	1−z	NUM
ma-136	656	25	)	)	PUNCT
ma-136	656	26	)	)	PUNCT
ma-136	656	27	7	7	X
ma-136	656	28	}	}	PUNCT
ma-136	656	29	f	f	NOUN
ma-136	656	30	′′+k1	′′+k1	X
ma-136	656	31	(	(	PUNCT
ma-136	656	32	z	z	NOUN
ma-136	656	33	)	)	PUNCT
ma-136	656	34	exp4	exp4	NOUN
ma-136	656	35	{	{	PUNCT
ma-136	656	36	2	2	NUM
ma-136	656	37	(	(	PUNCT
ma-136	656	38	log2	log2	PROPN
ma-136	656	39	(	(	PUNCT
ma-136	656	40	1	1	NUM
ma-136	656	41	1−z	1−z	NUM
ma-136	656	42	)	)	PUNCT
ma-136	656	43	)	)	PUNCT
ma-136	656	44	7	7	X
ma-136	656	45	}	}	PUNCT
ma-136	656	46	f	f	NOUN
ma-136	656	47	′	′	NUM
ma-136	657	1	+	+	PROPN
ma-136	657	2	k0	k0	PROPN
ma-136	657	3	(	(	PUNCT
ma-136	657	4	z	z	NOUN
ma-136	657	5	)	)	PUNCT
ma-136	657	6	exp4	exp4	NOUN
ma-136	657	7	{	{	PUNCT
ma-136	657	8	5	5	NUM
ma-136	657	9	(	(	PUNCT
ma-136	657	10	log2	log2	PROPN
ma-136	657	11	(	(	PUNCT
ma-136	657	12	1	1	NUM
ma-136	657	13	1−z	1−z	NUM
ma-136	657	14	)	)	PUNCT
ma-136	657	15	)	)	PUNCT
ma-136	657	16	7	7	X
ma-136	657	17	}	}	PUNCT
ma-136	657	18	f	f	NOUN
ma-136	657	19	=	=	SYM
ma-136	657	20	0	0	NUM
ma-136	657	21	,	,	PUNCT
ma-136	657	22	(	(	PUNCT
ma-136	657	23	6.2	6.2	NUM
ma-136	657	24	)	)	PUNCT
ma-136	657	25	where	where	SCONJ
ma-136	657	26	k0	k0	PROPN
ma-136	657	27	,	,	PUNCT
ma-136	657	28	k1	k1	PROPN
ma-136	657	29	and	and	CCONJ
ma-136	657	30	k2	k2	PROPN
ma-136	657	31	are	be	AUX
ma-136	657	32	analytic	analytic	ADJ
ma-136	657	33	functions	function	NOUN
ma-136	657	34	in	in	ADP
ma-136	657	35	the	the	DET
ma-136	657	36	unit	unit	NOUN
ma-136	657	37	discd	discd	VERB
ma-136	657	38	such	such	ADJ
ma-136	657	39	that	that	DET
ma-136	657	40	|k0|	|k0|	NOUN
ma-136	657	41	>	>	X
ma-136	657	42	1	1	NUM
ma-136	657	43	,	,	PUNCT
ma-136	657	44	|k1|	|k1|	NOUN
ma-136	657	45	<	<	X
ma-136	657	46	1	1	NUM
ma-136	657	47	,	,	PUNCT
ma-136	657	48	|k2|	|k2|	ADV
ma-136	657	49	<	<	X
ma-136	657	50	1and	1and	NUM
ma-136	657	51	max	max	PROPN
ma-136	657	52	{	{	PUNCT
ma-136	657	53	σm,[4,3	σm,[4,3	PROPN
ma-136	657	54	]	]	X
ma-136	657	55	(	(	PUNCT
ma-136	657	56	k0	k0	PROPN
ma-136	657	57	)	)	PUNCT
ma-136	657	58	,	,	PUNCT
ma-136	657	59	σm,[4,3	σm,[4,3	PROPN
ma-136	657	60	]	]	X
ma-136	657	61	(	(	PUNCT
ma-136	657	62	k1	k1	NOUN
ma-136	657	63	)	)	PUNCT
ma-136	657	64	,	,	PUNCT
ma-136	657	65	σm,[4,3	σm,[4,3	PROPN
ma-136	657	66	]	]	X
ma-136	657	67	(	(	PUNCT
ma-136	657	68	k2	k2	NOUN
ma-136	657	69	)	)	PUNCT
ma-136	657	70	}	}	PUNCT
ma-136	657	71	<	<	X
ma-136	657	72	7	7	X
ma-136	657	73	.	.	PUNCT
ma-136	657	74	in	in	ADP
ma-136	657	75	the	the	DET
ma-136	657	76	equation	equation	NOUN
ma-136	657	77	(	(	PUNCT
ma-136	657	78	6.2	6.2	NUM
ma-136	657	79	)	)	PUNCT
ma-136	657	80	,	,	PUNCT
ma-136	657	81	we	we	PRON
ma-136	657	82	have	have	VERB
ma-136	657	83	a0	a0	NOUN
ma-136	657	84	(	(	PUNCT
ma-136	657	85	z	z	NOUN
ma-136	657	86	)	)	PUNCT
ma-136	657	87	=	=	SYM
ma-136	657	88	k0	k0	PROPN
ma-136	657	89	(	(	PUNCT
ma-136	657	90	z	z	NOUN
ma-136	657	91	)	)	PUNCT
ma-136	657	92	exp4	exp4	NOUN
ma-136	657	93	{	{	PUNCT
ma-136	657	94	5	5	NUM
ma-136	657	95	(	(	PUNCT
ma-136	657	96	log2	log2	PROPN
ma-136	657	97	(	(	PUNCT
ma-136	657	98	1	1	NUM
ma-136	657	99	1−z	1−z	NUM
ma-136	657	100	)	)	PUNCT
ma-136	657	101	)	)	PUNCT
ma-136	657	102	7	7	X
ma-136	657	103	}	}	PUNCT
ma-136	657	104	,	,	PUNCT
ma-136	657	105	a1	a1	NOUN
ma-136	657	106	(	(	PUNCT
ma-136	657	107	z	z	NOUN
ma-136	657	108	)	)	PUNCT
ma-136	657	109	=	=	SYM
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ma-136	657	111	(	(	PUNCT
ma-136	657	112	z	z	NOUN
ma-136	657	113	)	)	PUNCT
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ma-136	657	117	(	(	PUNCT
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ma-136	657	119	(	(	PUNCT
ma-136	657	120	1	1	NUM
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ma-136	657	123	)	)	PUNCT
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ma-136	657	126	,	,	PUNCT
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ma-136	657	128	(	(	PUNCT
ma-136	657	129	z	z	NOUN
ma-136	657	130	)	)	PUNCT
ma-136	657	131	=	=	SYM
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ma-136	657	133	(	(	PUNCT
ma-136	657	134	z	z	NOUN
ma-136	657	135	)	)	PUNCT
ma-136	657	136	exp4	exp4	NOUN
ma-136	657	137	{	{	PUNCT
ma-136	657	138	(	(	PUNCT
ma-136	657	139	log2	log2	PROPN
ma-136	657	140	(	(	PUNCT
ma-136	657	141	1	1	NUM
ma-136	657	142	1−z	1−z	NUM
ma-136	657	143	)	)	PUNCT
ma-136	657	144	)	)	PUNCT
ma-136	657	145	7	7	NUM
ma-136	657	146	}	}	PUNCT
ma-136	657	147	.	.	PUNCT
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ma-136	658	2	max	max	PROPN
ma-136	658	3	{	{	PUNCT
ma-136	658	4	σm,[4,3	σm,[4,3	PROPN
ma-136	658	5	]	]	X
ma-136	658	6	(	(	PUNCT
ma-136	658	7	a0	a0	PROPN
ma-136	658	8	)	)	PUNCT
ma-136	658	9	,	,	PUNCT
ma-136	658	10	σm,[4,3	σm,[4,3	PROPN
ma-136	658	11	]	]	X
ma-136	658	12	(	(	PUNCT
ma-136	658	13	a1	a1	PROPN
ma-136	658	14	)	)	PUNCT
ma-136	658	15	,	,	PUNCT
ma-136	658	16	σm,[4,3	σm,[4,3	PROPN
ma-136	658	17	]	]	X
ma-136	658	18	(	(	PUNCT
ma-136	658	19	a2	a2	PROPN
ma-136	658	20	)	)	PUNCT
ma-136	658	21	}	}	PUNCT
ma-136	658	22	=	=	SYM
ma-136	658	23	7	7	X
ma-136	658	24	.	.	X
ma-136	658	25	let	let	VERB
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ma-136	658	27	=	=	PRON
ma-136	658	28	{	{	PUNCT
ma-136	658	29	z	z	NOUN
ma-136	658	30	∈	∈	PROPN
ma-136	658	31	c	c	NOUN
ma-136	658	32	:	:	PUNCT
ma-136	658	33	|z	|z	PROPN
ma-136	659	1	|	|	ADV
ma-136	659	2	=	=	SYM
ma-136	659	3	r	r	NOUN
ma-136	659	4	<	<	X
ma-136	659	5	1	1	NUM
ma-136	659	6	and	and	CCONJ
ma-136	659	7	arg	arg	NOUN
ma-136	659	8	z	z	NOUN
ma-136	659	9	=	=	SYM
ma-136	659	10	0	0	NUM
ma-136	659	11	}	}	PUNCT
ma-136	659	12	⊂	⊂	PROPN
ma-136	660	1	d	d	AUX
ma-136	660	2	be	be	AUX
ma-136	660	3	a	a	DET
ma-136	660	4	set	set	NOUN
ma-136	660	5	of	of	ADP
ma-136	660	6	complex	complex	ADJ
ma-136	660	7	numbers	number	NOUN
ma-136	660	8	satisfying	satisfy	VERB
ma-136	660	9	densd	densd	PROPN
ma-136	660	10	{	{	PUNCT
ma-136	660	11	|z	|z	PROPN
ma-136	661	1	|	|	ADV
ma-136	661	2	:	:	PUNCT
ma-136	661	3	z	z	PROPN
ma-136	661	4	∈	∈	PROPN
ma-136	662	1	h	h	NOUN
ma-136	662	2	}	}	PUNCT
ma-136	662	3	=	=	SYM
ma-136	662	4	1	1	NUM
ma-136	662	5	>	>	X
ma-136	662	6	0	0	X
ma-136	662	7	.	.	PUNCT
ma-136	663	1	then	then	ADV
ma-136	663	2	|a0	|a0	PROPN
ma-136	663	3	(	(	PUNCT
ma-136	663	4	z)|	z)|	NOUN
ma-136	663	5	=	=	SYM
ma-136	663	6	|k0	|k0	NOUN
ma-136	663	7	(	(	PUNCT
ma-136	663	8	z)|	z)|	NOUN
ma-136	663	9	∣∣∣exp4	∣∣∣exp4	PUNCT
ma-136	663	10	{	{	PUNCT
ma-136	663	11	5	5	NUM
ma-136	663	12	(	(	PUNCT
ma-136	663	13	log2	log2	PROPN
ma-136	663	14	(	(	PUNCT
ma-136	663	15	1	1	NUM
ma-136	663	16	1−z	1−z	NUM
ma-136	663	17	)	)	PUNCT
ma-136	663	18	)	)	PUNCT
ma-136	663	19	7}∣∣∣	7}∣∣∣	NUM
ma-136	664	1	>	>	X
ma-136	664	2	exp4	exp4	NOUN
ma-136	664	3	{	{	PUNCT
ma-136	664	4	5	5	NUM
ma-136	664	5	(	(	PUNCT
ma-136	664	6	log2	log2	PROPN
ma-136	664	7	(	(	PUNCT
ma-136	664	8	1	1	NUM
ma-136	664	9	1−r	1−r	NUM
ma-136	664	10	)	)	PUNCT
ma-136	664	11	)	)	PUNCT
ma-136	664	12	7	7	X
ma-136	664	13	}	}	PUNCT
ma-136	664	14	⇒	⇒	NOUN
ma-136	664	15	log4	log4	NOUN
ma-136	664	16	|a0	|a0	PROPN
ma-136	664	17	(	(	PUNCT
ma-136	664	18	z)|	z)|	X
ma-136	664	19	(	(	PUNCT
ma-136	664	20	log2	log2	PROPN
ma-136	664	21	(	(	PUNCT
ma-136	664	22	1	1	NUM
ma-136	664	23	1−r	1−r	NUM
ma-136	664	24	)	)	PUNCT
ma-136	664	25	)	)	PUNCT
ma-136	664	26	7	7	NUM
ma-136	664	27	>	>	SYM
ma-136	664	28	5⇒	5⇒	NUM
ma-136	664	29	lim	lim	PROPN
ma-136	664	30	inf	inf	PROPN
ma-136	664	31	r→1−,z∈h	r→1−,z∈h	PROPN
ma-136	664	32	log4	log4	PROPN
ma-136	664	33	|a0	|a0	PROPN
ma-136	664	34	(	(	PUNCT
ma-136	664	35	z)|	z)|	X
ma-136	664	36	(	(	PUNCT
ma-136	664	37	log2	log2	PROPN
ma-136	664	38	(	(	PUNCT
ma-136	664	39	1	1	NUM
ma-136	664	40	1−r	1−r	NUM
ma-136	664	41	)	)	PUNCT
ma-136	664	42	)	)	PUNCT
ma-136	664	43	7	7	NUM
ma-136	664	44	≥	≥	NOUN
ma-136	664	45	5	5	NUM
ma-136	664	46	>	>	SYM
ma-136	664	47	2	2	NUM
ma-136	664	48	,	,	PUNCT
ma-136	664	49	and	and	CCONJ
ma-136	664	50	|a1	|a1	NOUN
ma-136	664	51	(	(	PUNCT
ma-136	664	52	z)|	z)|	NOUN
ma-136	664	53	=	=	SYM
ma-136	664	54	|k1	|k1	NOUN
ma-136	664	55	(	(	PUNCT
ma-136	664	56	z)|	z)|	X
ma-136	664	57	∣∣∣∣∣exp4	∣∣∣∣∣exp4	PROPN
ma-136	664	58	{	{	PUNCT
ma-136	664	59	2	2	NUM
ma-136	664	60	(	(	PUNCT
ma-136	664	61	log2	log2	PROPN
ma-136	664	62	(	(	PUNCT
ma-136	664	63	1	1	NUM
ma-136	664	64	1−	1−	NUM
ma-136	664	65	z	z	NOUN
ma-136	664	66	)	)	PUNCT
ma-136	664	67	)	)	PUNCT
ma-136	664	68	7}∣∣∣∣∣	7}∣∣∣∣∣	PROPN
ma-136	664	69	≤	≤	NOUN
ma-136	664	70	exp4	exp4	NOUN
ma-136	664	71	{	{	PUNCT
ma-136	664	72	2	2	NUM
ma-136	664	73	(	(	PUNCT
ma-136	664	74	log2	log2	PROPN
ma-136	664	75	(	(	PUNCT
ma-136	664	76	1	1	NUM
ma-136	664	77	1−	1−	NUM
ma-136	664	78	r	r	NOUN
ma-136	664	79	)	)	PUNCT
ma-136	664	80	)	)	PUNCT
ma-136	664	81	7	7	X
ma-136	664	82	}	}	PUNCT
ma-136	664	83	|a2	|a2	NOUN
ma-136	664	84	(	(	PUNCT
ma-136	664	85	z)|	z)|	NOUN
ma-136	664	86	=	=	SYM
ma-136	664	87	|k2	|k2	PROPN
ma-136	664	88	(	(	PUNCT
ma-136	664	89	z)|	z)|	X
ma-136	664	90	∣∣∣∣∣exp4	∣∣∣∣∣exp4	PROPN
ma-136	664	91	{	{	PUNCT
ma-136	664	92	(	(	PUNCT
ma-136	664	93	log2	log2	PROPN
ma-136	664	94	(	(	PUNCT
ma-136	664	95	1	1	NUM
ma-136	664	96	1−	1−	NUM
ma-136	664	97	z	z	NOUN
ma-136	664	98	)	)	PUNCT
ma-136	664	99	)	)	PUNCT
ma-136	664	100	7}∣∣∣∣∣	7}∣∣∣∣∣	PROPN
ma-136	664	101	≤	≤	NOUN
ma-136	664	102	exp4	exp4	NOUN
ma-136	664	103	{	{	PUNCT
ma-136	664	104	2	2	NUM
ma-136	664	105	(	(	PUNCT
ma-136	664	106	log2	log2	PROPN
ma-136	664	107	(	(	PUNCT
ma-136	664	108	1	1	NUM
ma-136	664	109	1−	1−	NUM
ma-136	664	110	r	r	NOUN
ma-136	664	111	)	)	PUNCT
ma-136	664	112	)	)	PUNCT
ma-136	664	113	7	7	X
ma-136	664	114	}	}	PUNCT
ma-136	664	115	https://doi.org/10.28924/ada/ma.3.10	https://doi.org/10.28924/ada/ma.3.10	ADV
ma-136	664	116	eur	eur	NOUN
ma-136	664	117	.	.	PUNCT
ma-136	665	1	j.	j.	PROPN
ma-136	665	2	math	math	PROPN
ma-136	665	3	.	.	PUNCT
ma-136	666	1	anal	anal	PROPN
ma-136	666	2	.	.	PUNCT
ma-136	667	1	10.28924	10.28924	NUM
ma-136	667	2	/	/	SYM
ma-136	667	3	ada	ada	NOUN
ma-136	667	4	/	/	SYM
ma-136	667	5	ma.3.10	ma.3.10	NOUN
ma-136	667	6	26as	26as	ADJ
ma-136	667	7	r	r	NOUN
ma-136	667	8	→	→	SYM
ma-136	667	9	1−	1−	NUM
ma-136	667	10	for	for	ADP
ma-136	667	11	z	z	PROPN
ma-136	667	12	∈	∈	PROPN
ma-136	667	13	h.	h.	NOUN
ma-136	667	14	it	it	PRON
ma-136	667	15	is	be	AUX
ma-136	667	16	clear	clear	ADJ
ma-136	667	17	that	that	SCONJ
ma-136	667	18	the	the	DET
ma-136	667	19	conditions	condition	NOUN
ma-136	667	20	of	of	ADP
ma-136	667	21	theorem	theorem	ADJ
ma-136	667	22	1.5	1.5	NUM
ma-136	667	23	hold	hold	NOUN
ma-136	667	24	with	with	ADP
ma-136	667	25	α	α	NOUN
ma-136	667	26	=	=	SYM
ma-136	667	27	2	2	NUM
ma-136	667	28	,	,	PUNCT
ma-136	667	29	µ	µ	X
ma-136	667	30	=	=	SYM
ma-136	667	31	7	7	NUM
ma-136	667	32	,	,	PUNCT
ma-136	667	33	p	p	NOUN
ma-136	667	34	=	=	PUNCT
ma-136	667	35	4and	4and	NUM
ma-136	667	36	q	q	NOUN
ma-136	667	37	=	=	SYM
ma-136	667	38	3	3	NUM
ma-136	667	39	on	on	ADP
ma-136	667	40	the	the	DET
ma-136	667	41	set	set	NOUN
ma-136	667	42	h.	h.	PROPN
ma-136	667	43	by	by	ADP
ma-136	667	44	theorem	theorem	NOUN
ma-136	667	45	1.11	1.11	NUM
ma-136	667	46	,	,	PUNCT
ma-136	667	47	every	every	DET
ma-136	667	48	meromorphic	meromorphic	ADJ
ma-136	667	49	(	(	PUNCT
ma-136	667	50	or	or	CCONJ
ma-136	667	51	analytic	analytic	ADJ
ma-136	667	52	)	)	PUNCT
ma-136	667	53	solution	solution	NOUN
ma-136	667	54	f	f	NOUN
ma-136	667	55	6≡	6≡	NUM
ma-136	667	56	0	0	NUM
ma-136	667	57	ofequation	ofequation	NOUN
ma-136	667	58	(	(	PUNCT
ma-136	667	59	6.2	6.2	NUM
ma-136	667	60	)	)	PUNCT
ma-136	667	61	satisfies	satisfy	VERB
ma-136	667	62	λ̄[4,3	λ̄[4,3	NOUN
ma-136	667	63	]	]	X
ma-136	667	64	(	(	PUNCT
ma-136	667	65	f	f	X
ma-136	667	66	(	(	PUNCT
ma-136	667	67	j	j	PROPN
ma-136	667	68	)	)	PUNCT
ma-136	667	69	−	−	PROPN
ma-136	667	70	z	z	NOUN
ma-136	667	71	)	)	PUNCT
ma-136	667	72	=	=	PUNCT
ma-136	668	1	λ̄[4,3	λ̄[4,3	X
ma-136	668	2	]	]	X
ma-136	668	3	(	(	PUNCT
ma-136	668	4	f	f	PROPN
ma-136	668	5	−	−	PROPN
ma-136	668	6	z	z	PROPN
ma-136	668	7	)	)	PUNCT
ma-136	668	8	=	=	SYM
ma-136	668	9	σ[4,3	σ[4,3	X
ma-136	668	10	]	]	PUNCT
ma-136	668	11	(	(	PUNCT
ma-136	668	12	f	f	X
ma-136	668	13	)	)	PUNCT
ma-136	669	1	=	=	NOUN
ma-136	669	2	∞	∞	NUM
ma-136	669	3	and	and	CCONJ
ma-136	669	4	λ̄[5,3	λ̄[5,3	PROPN
ma-136	669	5	]	]	X
ma-136	669	6	(	(	PUNCT
ma-136	669	7	f	f	X
ma-136	669	8	(	(	PUNCT
ma-136	669	9	j	j	PROPN
ma-136	669	10	)	)	PUNCT
ma-136	669	11	−	−	PROPN
ma-136	669	12	z	z	NOUN
ma-136	669	13	)	)	PUNCT
ma-136	670	1	=	=	PUNCT
ma-136	670	2	λ̄[5,3	λ̄[5,3	X
ma-136	670	3	]	]	X
ma-136	670	4	(	(	PUNCT
ma-136	670	5	f	f	X
ma-136	670	6	−	−	PROPN
ma-136	670	7	z	z	PROPN
ma-136	670	8	)	)	PUNCT
ma-136	670	9	=	=	SYM
ma-136	670	10	σ[5,3	σ[5,3	NOUN
ma-136	670	11	]	]	PUNCT
ma-136	670	12	(	(	PUNCT
ma-136	670	13	f	f	PROPN
ma-136	670	14	)	)	PUNCT
ma-136	670	15	≥	≥	NOUN
ma-136	670	16	7	7	NUM
ma-136	670	17	,	,	PUNCT
ma-136	670	18	(	(	PUNCT
ma-136	670	19	j	j	NOUN
ma-136	670	20	=	=	SYM
ma-136	670	21	1	1	NUM
ma-136	670	22	,	,	PUNCT
ma-136	670	23	2	2	NUM
ma-136	670	24	,	,	PUNCT
ma-136	670	25	...	...	PUNCT
ma-136	670	26	)	)	PUNCT
ma-136	670	27	.	.	PUNCT
ma-136	671	1	references	reference	NOUN
ma-136	671	2	[	[	X
ma-136	671	3	1	1	NUM
ma-136	671	4	]	]	PUNCT
ma-136	671	5	s.	s.	PROPN
ma-136	671	6	bank	bank	PROPN
ma-136	671	7	,	,	PUNCT
ma-136	671	8	general	general	ADJ
ma-136	671	9	theorem	theorem	NOUN
ma-136	671	10	concerning	concern	VERB
ma-136	671	11	the	the	DET
ma-136	671	12	growth	growth	NOUN
ma-136	671	13	of	of	ADP
ma-136	671	14	solutions	solution	NOUN
ma-136	671	15	of	of	ADP
ma-136	671	16	first	first	ADJ
ma-136	671	17	-	-	PUNCT
ma-136	671	18	order	order	NOUN
ma-136	671	19	algebraic	algebraic	PROPN
ma-136	671	20	differential	differential	NOUN
ma-136	671	21	equations	equation	NOUN
ma-136	671	22	.	.	PUNCT
ma-136	672	1	compos.math	compos.math	X
ma-136	672	2	.	.	NOUN
ma-136	673	1	25	25	NUM
ma-136	673	2	(	(	PUNCT
ma-136	673	3	1972	1972	NUM
ma-136	673	4	)	)	PUNCT
ma-136	673	5	61–70	61–70	NOUN
ma-136	673	6	.	.	PUNCT
ma-136	674	1	http://www.numdam.org/item/cm_1972__25_1_61_0.[2	http://www.numdam.org/item/cm_1972__25_1_61_0.[2	PROPN
ma-136	674	2	]	]	X
ma-136	674	3	b.	b.	PROPN
ma-136	674	4	belaïdi	belaïdi	PROPN
ma-136	674	5	,	,	PUNCT
ma-136	674	6	estimation	estimation	NOUN
ma-136	674	7	of	of	ADP
ma-136	674	8	the	the	DET
ma-136	674	9	hyper	hyper	NOUN
ma-136	674	10	-	-	NOUN
ma-136	674	11	order	order	NOUN
ma-136	674	12	of	of	ADP
ma-136	674	13	entire	entire	ADJ
ma-136	674	14	solutions	solution	NOUN
ma-136	674	15	of	of	ADP
ma-136	674	16	complex	complex	ADJ
ma-136	674	17	linear	linear	ADJ
ma-136	674	18	ordinary	ordinary	ADJ
ma-136	674	19	differential	differential	ADJ
ma-136	674	20	equations	equation	NOUN
ma-136	674	21	whosecoefficients	whosecoefficient	NOUN
ma-136	674	22	are	be	AUX
ma-136	674	23	entire	entire	ADJ
ma-136	674	24	functions	function	NOUN
ma-136	674	25	.	.	PUNCT
ma-136	675	1	electron	electron	PROPN
ma-136	675	2	.	.	PUNCT
ma-136	676	1	j.	j.	PROPN
ma-136	676	2	qual	qual	PROPN
ma-136	676	3	.	.	PROPN
ma-136	676	4	theory	theory	PROPN
ma-136	676	5	diff	diff	PROPN
ma-136	676	6	.	.	PUNCT
ma-136	677	1	equ	equ	PROPN
ma-136	677	2	.	.	PROPN
ma-136	677	3	2002	2002	NUM
ma-136	677	4	(	(	PUNCT
ma-136	677	5	2002	2002	NUM
ma-136	677	6	)	)	PUNCT
ma-136	677	7	5	5	NUM
ma-136	677	8	.	.	X
ma-136	677	9	http://real.mtak.hu/23284.[3	http://real.mtak.hu/23284.[3	PROPN
ma-136	677	10	]	]	PUNCT
ma-136	677	11	b.	b.	PROPN
ma-136	677	12	belaïdi	belaïdi	PROPN
ma-136	677	13	,	,	PUNCT
ma-136	677	14	growth	growth	NOUN
ma-136	677	15	of	of	ADP
ma-136	677	16	solutions	solution	NOUN
ma-136	677	17	to	to	PART
ma-136	677	18	linear	linear	VERB
ma-136	677	19	equations	equation	NOUN
ma-136	677	20	with	with	ADP
ma-136	677	21	analytic	analytic	ADJ
ma-136	677	22	coefficients	coefficient	NOUN
ma-136	677	23	of	of	ADP
ma-136	677	24	[	[	X
ma-136	677	25	p	p	X
ma-136	677	26	,	,	PUNCT
ma-136	677	27	q	q	X
ma-136	677	28	]	]	X
ma-136	677	29	-order	-order	NOUN
ma-136	677	30	in	in	ADP
ma-136	677	31	the	the	DET
ma-136	677	32	unit	unit	NOUN
ma-136	677	33	disc	disc	NOUN
ma-136	677	34	.	.	PUNCT
ma-136	677	35	electron	electron	PROPN
ma-136	677	36	.	.	PUNCT
ma-136	678	1	j.diff	j.diff	PROPN
ma-136	678	2	.	.	PUNCT
ma-136	679	1	equ	equ	PROPN
ma-136	679	2	.	.	PROPN
ma-136	679	3	2011	2011	NUM
ma-136	679	4	(	(	PUNCT
ma-136	679	5	2011	2011	NUM
ma-136	679	6	)	)	PUNCT
ma-136	679	7	156	156	NUM
ma-136	679	8	.	.	PUNCT
ma-136	680	1	http://ftp.gwdg.de/pub/emis/journals/ejde/volumes/2011/156/abstr.html.[4	http://ftp.gwdg.de/pub/emis/journals/ejde/volumes/2011/156/abstr.html.[4	NOUN
ma-136	680	2	]	]	X
ma-136	680	3	b.	b.	PROPN
ma-136	680	4	belaïdi	belaïdi	PROPN
ma-136	680	5	,	,	PUNCT
ma-136	680	6	growth	growth	NOUN
ma-136	680	7	and	and	CCONJ
ma-136	680	8	oscillation	oscillation	NOUN
ma-136	680	9	theory	theory	NOUN
ma-136	680	10	of	of	ADP
ma-136	680	11	[	[	X
ma-136	680	12	p	p	X
ma-136	680	13	,	,	PUNCT
ma-136	680	14	q]-order	q]-order	NOUN
ma-136	680	15	analytic	analytic	ADJ
ma-136	680	16	solutions	solution	NOUN
ma-136	680	17	of	of	ADP
ma-136	680	18	linear	linear	ADJ
ma-136	680	19	equations	equation	NOUN
ma-136	680	20	in	in	ADP
ma-136	680	21	the	the	DET
ma-136	680	22	unit	unit	NOUN
ma-136	680	23	disc	disc	NOUN
ma-136	680	24	.	.	PUNCT
ma-136	680	25	j.math	j.math	PROPN
ma-136	680	26	.	.	PUNCT
ma-136	681	1	anal	anal	ADJ
ma-136	681	2	.	.	PUNCT
ma-136	682	1	3	3	NUM
ma-136	682	2	(	(	PUNCT
ma-136	682	3	2012	2012	NUM
ma-136	682	4	)	)	PUNCT
ma-136	682	5	1	1	NUM
ma-136	682	6	-	-	SYM
ma-136	682	7	11.[5	11.[5	NUM
ma-136	682	8	]	]	PUNCT
ma-136	682	9	b.	b.	PROPN
ma-136	682	10	belaïdi	belaïdi	PROPN
ma-136	682	11	,	,	PUNCT
ma-136	682	12	on	on	ADP
ma-136	682	13	the	the	DET
ma-136	682	14	[	[	X
ma-136	682	15	p	p	X
ma-136	682	16	,	,	PUNCT
ma-136	682	17	q]-order	q]-order	NOUN
ma-136	682	18	of	of	ADP
ma-136	682	19	analytic	analytic	ADJ
ma-136	682	20	solutions	solution	NOUN
ma-136	682	21	of	of	ADP
ma-136	682	22	linear	linear	ADJ
ma-136	682	23	equations	equation	NOUN
ma-136	682	24	in	in	ADP
ma-136	682	25	the	the	DET
ma-136	682	26	unit	unit	NOUN
ma-136	682	27	disc	disc	NOUN
ma-136	682	28	.	.	PUNCT
ma-136	683	1	novi	novi	PROPN
ma-136	683	2	sad	sad	PROPN
ma-136	683	3	j.	j.	PROPN
ma-136	683	4	math	math	PROPN
ma-136	683	5	.	.	PUNCT
ma-136	684	1	42	42	NUM
ma-136	684	2	(	(	PUNCT
ma-136	684	3	2012)117–129.[6	2012)117–129.[6	NUM
ma-136	684	4	]	]	X
ma-136	684	5	l.	l.	PROPN
ma-136	684	6	g.	g.	PROPN
ma-136	684	7	bernal	bernal	PROPN
ma-136	684	8	,	,	PUNCT
ma-136	684	9	on	on	ADP
ma-136	684	10	growth	growth	NOUN
ma-136	684	11	k	k	PROPN
ma-136	684	12	-order	-order	PROPN
ma-136	684	13	of	of	ADP
ma-136	684	14	solutions	solution	NOUN
ma-136	684	15	of	of	ADP
ma-136	684	16	a	a	DET
ma-136	684	17	complex	complex	ADJ
ma-136	684	18	homogeneous	homogeneous	ADJ
ma-136	684	19	linear	linear	PROPN
ma-136	684	20	differential	differential	NOUN
ma-136	684	21	equation	equation	NOUN
ma-136	684	22	.	.	PUNCT
ma-136	685	1	proc	proc	PROPN
ma-136	685	2	.	.	PUNCT
ma-136	686	1	amer.math	amer.math	NUM
ma-136	686	2	.	.	PUNCT
ma-136	687	1	soc	soc	PROPN
ma-136	687	2	.	.	PUNCT
ma-136	688	1	101	101	NUM
ma-136	688	2	(	(	PUNCT
ma-136	688	3	1987	1987	NUM
ma-136	688	4	)	)	PUNCT
ma-136	688	5	317–322	317–322	NUM
ma-136	688	6	.	.	PUNCT
ma-136	689	1	https://doi.org/10.1090/s0002-9939-1987-0902549-5.[7	https://doi.org/10.1090/s0002-9939-1987-0902549-5.[7	PROPN
ma-136	689	2	]	]	PUNCT
ma-136	689	3	t.	t.	PROPN
ma-136	689	4	b.	b.	PROPN
ma-136	689	5	cao	cao	PROPN
ma-136	689	6	and	and	CCONJ
ma-136	689	7	h.	h.	PROPN
ma-136	689	8	x.	x.	PROPN
ma-136	689	9	yi	yi	PROPN
ma-136	689	10	,	,	PUNCT
ma-136	689	11	the	the	DET
ma-136	689	12	growth	growth	NOUN
ma-136	689	13	of	of	ADP
ma-136	689	14	solutions	solution	NOUN
ma-136	689	15	of	of	ADP
ma-136	689	16	linear	linear	PROPN
ma-136	689	17	differential	differential	ADJ
ma-136	689	18	equations	equation	NOUN
ma-136	689	19	with	with	ADP
ma-136	689	20	coefficients	coefficient	NOUN
ma-136	689	21	of	of	ADP
ma-136	689	22	iterated	iterated	ADJ
ma-136	689	23	order	order	NOUN
ma-136	689	24	inthe	inthe	DET
ma-136	689	25	unit	unit	NOUN
ma-136	689	26	disc	disc	NOUN
ma-136	689	27	.	.	PUNCT
ma-136	690	1	j.	j.	PROPN
ma-136	690	2	math	math	PROPN
ma-136	690	3	.	.	PUNCT
ma-136	691	1	anal	anal	PROPN
ma-136	691	2	.	.	PUNCT
ma-136	691	3	appl	appl	PROPN
ma-136	691	4	.	.	PUNCT
ma-136	692	1	319	319	NUM
ma-136	692	2	(	(	PUNCT
ma-136	692	3	2006	2006	NUM
ma-136	692	4	)	)	PUNCT
ma-136	692	5	278–294	278–294	NUM
ma-136	692	6	.	.	PUNCT
ma-136	693	1	https://doi.org/10.1016/j.jmaa.2005.09.050.[8	https://doi.org/10.1016/j.jmaa.2005.09.050.[8	PROPN
ma-136	693	2	]	]	PUNCT
ma-136	693	3	t.	t.	PROPN
ma-136	693	4	b.	b.	PROPN
ma-136	693	5	cao	cao	PROPN
ma-136	693	6	,	,	PUNCT
ma-136	693	7	the	the	DET
ma-136	693	8	growth	growth	NOUN
ma-136	693	9	,	,	PUNCT
ma-136	693	10	oscillation	oscillation	NOUN
ma-136	693	11	and	and	CCONJ
ma-136	693	12	fixed	fix	VERB
ma-136	693	13	points	point	NOUN
ma-136	693	14	of	of	ADP
ma-136	693	15	solutions	solution	NOUN
ma-136	693	16	of	of	ADP
ma-136	693	17	complex	complex	ADJ
ma-136	693	18	linear	linear	ADJ
ma-136	693	19	differential	differential	NOUN
ma-136	693	20	equations	equation	NOUN
ma-136	693	21	in	in	ADP
ma-136	693	22	the	the	DET
ma-136	693	23	unitdisc	unitdisc	NOUN
ma-136	693	24	.	.	PUNCT
ma-136	694	1	j.	j.	PROPN
ma-136	694	2	math	math	PROPN
ma-136	694	3	.	.	PUNCT
ma-136	695	1	anal	anal	PROPN
ma-136	695	2	.	.	PUNCT
ma-136	696	1	appl	appl	PROPN
ma-136	696	2	.	.	PUNCT
ma-136	697	1	352	352	NUM
ma-136	697	2	(	(	PUNCT
ma-136	697	3	2009	2009	NUM
ma-136	697	4	)	)	PUNCT
ma-136	698	1	739–748	739–748	NUM
ma-136	698	2	.	.	PUNCT
ma-136	699	1	https://doi.org/10.1016/j.jmaa.2008.11.033.[9	https://doi.org/10.1016/j.jmaa.2008.11.033.[9	NOUN
ma-136	699	2	]	]	PUNCT
ma-136	699	3	y.	y.	PROPN
ma-136	699	4	chen	chen	PROPN
ma-136	699	5	,	,	PUNCT
ma-136	699	6	g.	g.	PROPN
ma-136	699	7	t.	t.	PROPN
ma-136	699	8	deng	deng	PROPN
ma-136	699	9	,	,	PUNCT
ma-136	699	10	z.	z.	PROPN
ma-136	699	11	m.	m.	PROPN
ma-136	699	12	chen	chen	PROPN
ma-136	699	13	and	and	CCONJ
ma-136	699	14	w.	w.	PROPN
ma-136	699	15	w.	w.	PROPN
ma-136	699	16	wang	wang	PROPN
ma-136	699	17	,	,	PUNCT
ma-136	699	18	growth	growth	NOUN
ma-136	699	19	and	and	CCONJ
ma-136	699	20	fixed	fix	VERB
ma-136	699	21	points	point	NOUN
ma-136	699	22	of	of	ADP
ma-136	699	23	solutions	solution	NOUN
ma-136	699	24	and	and	CCONJ
ma-136	699	25	their	their	PRON
ma-136	699	26	arbitrary	arbitrary	ADJ
ma-136	699	27	-	-	PUNCT
ma-136	699	28	order	order	NOUN
ma-136	699	29	derivatives	derivative	NOUN
ma-136	699	30	of	of	ADP
ma-136	699	31	higher	high	ADJ
ma-136	699	32	-	-	PUNCT
ma-136	699	33	order	order	NOUN
ma-136	699	34	linear	linear	ADJ
ma-136	699	35	differential	differential	NOUN
ma-136	699	36	equations	equation	NOUN
ma-136	699	37	in	in	ADP
ma-136	699	38	the	the	DET
ma-136	699	39	unit	unit	NOUN
ma-136	699	40	disc	disc	NOUN
ma-136	699	41	.	.	PUNCT
ma-136	700	1	adv	adv	PROPN
ma-136	700	2	.	.	PUNCT
ma-136	701	1	diff	diff	PROPN
ma-136	701	2	.	.	PUNCT
ma-136	702	1	equ	equ	PROPN
ma-136	702	2	.	.	PROPN
ma-136	702	3	2021	2021	NUM
ma-136	702	4	(	(	PUNCT
ma-136	702	5	2021	2021	NUM
ma-136	702	6	)	)	PUNCT
ma-136	702	7	431	431	NUM
ma-136	702	8	.	.	PUNCT
ma-136	703	1	https://doi.org/10.1186/s13662-021-03579-3.[10	https://doi.org/10.1186/s13662-021-03579-3.[10	ADV
ma-136	703	2	]	]	PUNCT
ma-136	704	1	z.	z.	PROPN
ma-136	704	2	x.	x.	PROPN
ma-136	704	3	chen	chen	PROPN
ma-136	704	4	and	and	CCONJ
ma-136	704	5	c.	c.	PROPN
ma-136	704	6	c.	c.	PROPN
ma-136	704	7	yang	yang	PROPN
ma-136	704	8	,	,	PUNCT
ma-136	704	9	some	some	DET
ma-136	704	10	further	further	ADJ
ma-136	704	11	results	result	NOUN
ma-136	704	12	on	on	ADP
ma-136	704	13	the	the	DET
ma-136	704	14	zeros	zero	NOUN
ma-136	704	15	and	and	CCONJ
ma-136	704	16	growths	growth	NOUN
ma-136	704	17	of	of	ADP
ma-136	704	18	entire	entire	ADJ
ma-136	704	19	solutions	solution	NOUN
ma-136	704	20	of	of	ADP
ma-136	704	21	second	second	ADJ
ma-136	704	22	order	order	NOUN
ma-136	704	23	lineardifferential	lineardifferential	ADJ
ma-136	704	24	equations	equation	NOUN
ma-136	704	25	.	.	PUNCT
ma-136	705	1	kodai	kodai	PROPN
ma-136	705	2	math	math	PROPN
ma-136	705	3	.	.	PUNCT
ma-136	706	1	j.	j.	PROPN
ma-136	706	2	22	22	NUM
ma-136	706	3	(	(	PUNCT
ma-136	706	4	1999	1999	NUM
ma-136	706	5	)	)	PUNCT
ma-136	706	6	273–285	273–285	NUM
ma-136	706	7	.	.	PUNCT
ma-136	707	1	https://doi.org/10.2996/kmj/1138044047.[11	https://doi.org/10.2996/kmj/1138044047.[11	PROPN
ma-136	707	2	]	]	PUNCT
ma-136	707	3	i.	i.	PROPN
ma-136	707	4	chyzhykov	chyzhykov	PROPN
ma-136	707	5	,	,	PUNCT
ma-136	707	6	g.	g.	PROPN
ma-136	707	7	gundersen	gundersen	PROPN
ma-136	707	8	and	and	CCONJ
ma-136	707	9	j.	j.	PROPN
ma-136	707	10	heittokangas	heittokangas	PROPN
ma-136	707	11	,	,	PUNCT
ma-136	707	12	linear	linear	ADJ
ma-136	707	13	differential	differential	NOUN
ma-136	707	14	equations	equation	NOUN
ma-136	707	15	and	and	CCONJ
ma-136	707	16	logarithmic	logarithmic	ADJ
ma-136	707	17	derivative	derivative	ADJ
ma-136	707	18	estimates.proc	estimates.proc	NOUN
ma-136	707	19	.	.	PUNCT
ma-136	708	1	london	london	PROPN
ma-136	708	2	math	math	PROPN
ma-136	708	3	.	.	PUNCT
ma-136	709	1	soc	soc	PROPN
ma-136	709	2	.	.	PUNCT
ma-136	710	1	(	(	PUNCT
ma-136	710	2	3	3	X
ma-136	710	3	)	)	PUNCT
ma-136	710	4	86	86	NUM
ma-136	710	5	(	(	PUNCT
ma-136	710	6	2003	2003	NUM
ma-136	710	7	)	)	PUNCT
ma-136	711	1	735–754	735–754	NUM
ma-136	711	2	.	.	PUNCT
ma-136	712	1	https://doi.org/10.1112/s0024611502013965.[12	https://doi.org/10.1112/s0024611502013965.[12	X
ma-136	712	2	]	]	X
ma-136	712	3	w.	w.	PROPN
ma-136	712	4	k.	k.	PROPN
ma-136	712	5	hayman	hayman	PROPN
ma-136	712	6	,	,	PUNCT
ma-136	712	7	meromorphic	meromorphic	ADJ
ma-136	712	8	functions	function	NOUN
ma-136	712	9	.	.	PUNCT
ma-136	713	1	oxford	oxford	PROPN
ma-136	713	2	mathematical	mathematical	PROPN
ma-136	713	3	monographs	monograph	NOUN
ma-136	713	4	,	,	PUNCT
ma-136	713	5	clarendon	clarendon	PROPN
ma-136	713	6	press	press	NOUN
ma-136	713	7	,	,	PUNCT
ma-136	713	8	oxford	oxford	PROPN
ma-136	713	9	,	,	PUNCT
ma-136	713	10	1964.[13	1964.[13	NUM
ma-136	713	11	]	]	PUNCT
ma-136	713	12	j.	j.	PROPN
ma-136	713	13	heittokangas	heittokangas	PROPN
ma-136	713	14	,	,	PUNCT
ma-136	713	15	on	on	ADP
ma-136	713	16	complex	complex	ADJ
ma-136	713	17	differential	differential	ADJ
ma-136	713	18	equations	equation	NOUN
ma-136	713	19	in	in	ADP
ma-136	713	20	the	the	DET
ma-136	713	21	unit	unit	NOUN
ma-136	713	22	disc	disc	NOUN
ma-136	713	23	.	.	PUNCT
ma-136	714	1	ann	ann	PROPN
ma-136	714	2	.	.	PUNCT
ma-136	714	3	acad	acad	PROPN
ma-136	714	4	.	.	PUNCT
ma-136	715	1	sci	sci	PROPN
ma-136	715	2	.	.	PUNCT
ma-136	715	3	fenn	fenn	PROPN
ma-136	715	4	.	.	PUNCT
ma-136	715	5	math	math	PROPN
ma-136	715	6	.	.	PUNCT
ma-136	716	1	diss	diss	PROPN
ma-136	716	2	.	.	PROPN
ma-136	717	1	122	122	NUM
ma-136	717	2	(	(	PUNCT
ma-136	717	3	2000)1–54.[14	2000)1–54.[14	PROPN
ma-136	717	4	]	]	X
ma-136	717	5	h.	h.	PROPN
ma-136	717	6	hu	hu	PROPN
ma-136	717	7	and	and	CCONJ
ma-136	717	8	x.	x.	PROPN
ma-136	717	9	m.	m.	PROPN
ma-136	717	10	zheng	zheng	PROPN
ma-136	717	11	,	,	PUNCT
ma-136	717	12	growth	growth	NOUN
ma-136	717	13	of	of	ADP
ma-136	717	14	solutions	solution	NOUN
ma-136	717	15	of	of	ADP
ma-136	717	16	linear	linear	PROPN
ma-136	717	17	differential	differential	ADJ
ma-136	717	18	equations	equation	NOUN
ma-136	717	19	with	with	ADP
ma-136	717	20	analytic	analytic	ADJ
ma-136	717	21	coefficients	coefficient	NOUN
ma-136	717	22	of	of	ADP
ma-136	717	23	[	[	X
ma-136	717	24	p	p	X
ma-136	717	25	,	,	PUNCT
ma-136	717	26	q]-orderin	q]-orderin	NOUN
ma-136	717	27	the	the	DET
ma-136	717	28	unit	unit	NOUN
ma-136	717	29	disc	disc	PROPN
ma-136	717	30	.	.	PUNCT
ma-136	718	1	electron	electron	PROPN
ma-136	718	2	.	.	PUNCT
ma-136	719	1	j.	j.	PROPN
ma-136	719	2	diff	diff	PROPN
ma-136	719	3	.	.	PUNCT
ma-136	720	1	equ	equ	PROPN
ma-136	720	2	.	.	PROPN
ma-136	720	3	2014	2014	NUM
ma-136	720	4	(	(	PUNCT
ma-136	720	5	2014	2014	NUM
ma-136	720	6	)	)	PUNCT
ma-136	721	1	204.[15	204.[15	NUM
ma-136	721	2	]	]	X
ma-136	721	3	o.	o.	PROPN
ma-136	721	4	p.	p.	PROPN
ma-136	721	5	juneja	juneja	PROPN
ma-136	721	6	,	,	PUNCT
ma-136	721	7	g.	g.	PROPN
ma-136	721	8	p.	p.	PROPN
ma-136	721	9	kapoor	kapoor	PROPN
ma-136	721	10	and	and	CCONJ
ma-136	721	11	s.	s.	PROPN
ma-136	721	12	k.	k.	PROPN
ma-136	721	13	bajpai	bajpai	PROPN
ma-136	721	14	,	,	PUNCT
ma-136	721	15	on	on	ADP
ma-136	721	16	the	the	DET
ma-136	721	17	(	(	PUNCT
ma-136	721	18	p	p	NOUN
ma-136	721	19	,	,	PUNCT
ma-136	721	20	q)-order	q)-order	PUNCT
ma-136	721	21	and	and	CCONJ
ma-136	721	22	lower	low	ADJ
ma-136	721	23	(	(	PUNCT
ma-136	721	24	p	p	NOUN
ma-136	721	25	,	,	PUNCT
ma-136	721	26	q)-order	q)-order	NOUN
ma-136	721	27	of	of	ADP
ma-136	721	28	an	an	DET
ma-136	721	29	entire	entire	ADJ
ma-136	721	30	function	function	NOUN
ma-136	721	31	.	.	PUNCT
ma-136	722	1	j.	j.	PROPN
ma-136	722	2	reineangew	reineangew	PROPN
ma-136	722	3	.	.	PUNCT
ma-136	723	1	math	math	NOUN
ma-136	723	2	.	.	PUNCT
ma-136	724	1	282	282	NUM
ma-136	724	2	(	(	PUNCT
ma-136	724	3	1976	1976	NUM
ma-136	724	4	)	)	PUNCT
ma-136	724	5	53–67	53–67	NUM
ma-136	724	6	.	.	PUNCT
ma-136	725	1	https://doi.org/10.1515/crll.1977.290.180.[16	https://doi.org/10.1515/crll.1977.290.180.[16	PROPN
ma-136	725	2	]	]	PUNCT
ma-136	726	1	o.	o.	PROPN
ma-136	726	2	p.	p.	PROPN
ma-136	726	3	juneja	juneja	PROPN
ma-136	726	4	,	,	PUNCT
ma-136	726	5	g.	g.	PROPN
ma-136	726	6	p.	p.	PROPN
ma-136	726	7	kapoor	kapoor	PROPN
ma-136	726	8	and	and	CCONJ
ma-136	726	9	s.	s.	PROPN
ma-136	726	10	k.	k.	PROPN
ma-136	726	11	bajpai	bajpai	PROPN
ma-136	726	12	,	,	PUNCT
ma-136	726	13	on	on	ADP
ma-136	726	14	the	the	DET
ma-136	726	15	(	(	PUNCT
ma-136	726	16	p	p	NOUN
ma-136	726	17	,	,	PUNCT
ma-136	726	18	q)-type	q)-type	PUNCT
ma-136	726	19	and	and	CCONJ
ma-136	726	20	lower	low	ADJ
ma-136	726	21	(	(	PUNCT
ma-136	726	22	p	p	NOUN
ma-136	726	23	,	,	PUNCT
ma-136	726	24	q)-type	q)-type	PUNCT
ma-136	726	25	of	of	ADP
ma-136	726	26	an	an	DET
ma-136	726	27	entire	entire	ADJ
ma-136	726	28	function	function	NOUN
ma-136	726	29	.	.	PUNCT
ma-136	727	1	j.	j.	PROPN
ma-136	727	2	reineangew	reineangew	PROPN
ma-136	727	3	.	.	PUNCT
ma-136	728	1	math	math	NOUN
ma-136	728	2	.	.	PUNCT
ma-136	729	1	290	290	NUM
ma-136	729	2	(	(	PUNCT
ma-136	729	3	1977	1977	NUM
ma-136	729	4	)	)	PUNCT
ma-136	729	5	385	385	NUM
ma-136	729	6	-	-	SYM
ma-136	729	7	405	405	NUM
ma-136	729	8	.	.	PUNCT
ma-136	730	1	https://doi.org/10.1515/crll.1977.290.180.[17	https://doi.org/10.1515/crll.1977.290.180.[17	PROPN
ma-136	730	2	]	]	PUNCT
ma-136	730	3	i.	i.	PROPN
ma-136	730	4	laine	laine	PROPN
ma-136	730	5	,	,	PUNCT
ma-136	730	6	complex	complex	ADJ
ma-136	730	7	differential	differential	ADJ
ma-136	730	8	equations	equation	NOUN
ma-136	730	9	.	.	PUNCT
ma-136	731	1	handbook	handbook	NOUN
ma-136	731	2	of	of	ADP
ma-136	731	3	differential	differential	ADJ
ma-136	731	4	equations	equation	NOUN
ma-136	731	5	:	:	PUNCT
ma-136	731	6	ordinary	ordinary	ADJ
ma-136	731	7	differential	differential	ADJ
ma-136	731	8	equations	equation	NOUN
ma-136	731	9	.	.	PUNCT
ma-136	732	1	vol	vol	NOUN
ma-136	732	2	.	.	PUNCT
ma-136	733	1	iv,269–363	iv,269–363	ADJ
ma-136	733	2	,	,	PUNCT
ma-136	733	3	handb	handb	NOUN
ma-136	733	4	.	.	PUNCT
ma-136	733	5	differ	differ	VERB
ma-136	733	6	.	.	PUNCT
ma-136	734	1	equ	equ	PROPN
ma-136	734	2	.	.	PROPN
ma-136	734	3	,	,	PUNCT
ma-136	734	4	elsevier	elsevier	PROPN
ma-136	734	5	/	/	SYM
ma-136	734	6	north	north	PROPN
ma-136	734	7	-	-	PUNCT
ma-136	734	8	holland	holland	PROPN
ma-136	734	9	,	,	PUNCT
ma-136	734	10	amsterdam	amsterdam	PROPN
ma-136	734	11	,	,	PUNCT
ma-136	734	12	2008	2008	NUM
ma-136	734	13	.	.	PUNCT
ma-136	735	1	https://doi.org/10.28924/ada/ma.3.10	https://doi.org/10.28924/ada/ma.3.10	ADV
ma-136	735	2	http://www.numdam.org/item/cm_1972__25_1_61_0	http://www.numdam.org/item/cm_1972__25_1_61_0	X
ma-136	735	3	http://real.mtak.hu/23284	http://real.mtak.hu/23284	PROPN
ma-136	735	4	http://ftp.gwdg.de/pub/emis/journals/ejde/volumes/2011/156/abstr.html	http://ftp.gwdg.de/pub/emis/journals/ejde/volumes/2011/156/abstr.html	NUM
ma-136	736	1	https://doi.org/10.1090/s0002-9939-1987-0902549-5	https://doi.org/10.1090/s0002-9939-1987-0902549-5	NOUN
ma-136	736	2	https://doi.org/10.1016/j.jmaa.2005.09.050	https://doi.org/10.1016/j.jmaa.2005.09.050	PROPN
ma-136	736	3	https://doi.org/10.1016/j.jmaa.2008.11.033	https://doi.org/10.1016/j.jmaa.2008.11.033	VERB
ma-136	736	4	https://doi.org/10.1186/s13662-021-03579-3	https://doi.org/10.1186/s13662-021-03579-3	NUM
ma-136	736	5	https://doi.org/10.2996/kmj/1138044047	https://doi.org/10.2996/kmj/1138044047	VERB
ma-136	737	1	https://doi.org/10.1112/s0024611502013965	https://doi.org/10.1112/s0024611502013965	PRON
ma-136	737	2	https://doi.org/10.1515/crll.1977.290.180	https://doi.org/10.1515/crll.1977.290.180	PROPN
ma-136	737	3	https://doi.org/10.1515/crll.1977.290.180	https://doi.org/10.1515/crll.1977.290.180	PROPN
ma-136	737	4	eur	eur	PROPN
ma-136	737	5	.	.	PUNCT
ma-136	738	1	j.	j.	PROPN
ma-136	738	2	math	math	PROPN
ma-136	738	3	.	.	PUNCT
ma-136	739	1	anal	anal	PROPN
ma-136	739	2	.	.	PUNCT
ma-136	740	1	10.28924	10.28924	NUM
ma-136	740	2	/	/	SYM
ma-136	740	3	ada	ada	NOUN
ma-136	740	4	/	/	SYM
ma-136	740	5	ma.3.10	ma.3.10	NOUN
ma-136	740	6	27	27	NUM
ma-136	741	1	[	[	SYM
ma-136	741	2	18	18	NUM
ma-136	741	3	]	]	PUNCT
ma-136	741	4	z.	z.	PROPN
ma-136	741	5	latreuch	latreuch	PROPN
ma-136	741	6	and	and	CCONJ
ma-136	741	7	b.	b.	PROPN
ma-136	741	8	belaïdi	belaïdi	PROPN
ma-136	741	9	,	,	PUNCT
ma-136	741	10	linear	linear	ADJ
ma-136	741	11	differential	differential	ADJ
ma-136	741	12	equations	equation	NOUN
ma-136	741	13	with	with	ADP
ma-136	741	14	analytic	analytic	ADJ
ma-136	741	15	coefficients	coefficient	NOUN
ma-136	741	16	of	of	ADP
ma-136	741	17	[	[	X
ma-136	741	18	p	p	X
ma-136	741	19	,	,	PUNCT
ma-136	741	20	q]-order	q]-order	NOUN
ma-136	741	21	in	in	ADP
ma-136	741	22	the	the	DET
ma-136	741	23	unit	unit	NOUN
ma-136	741	24	disc.sarajevo	disc.sarajevo	PROPN
ma-136	741	25	j.	j.	PROPN
ma-136	741	26	math	math	PROPN
ma-136	741	27	.	.	PUNCT
ma-136	742	1	9	9	NUM
ma-136	742	2	(	(	PUNCT
ma-136	742	3	2013	2013	NUM
ma-136	742	4	)	)	PUNCT
ma-136	742	5	71–84	71–84	NOUN
ma-136	742	6	.	.	PUNCT
ma-136	743	1	http://doi.org/10.5644/sjm.09.1.06.[19	http://doi.org/10.5644/sjm.09.1.06.[19	NOUN
ma-136	743	2	]	]	PUNCT
ma-136	744	1	y.	y.	PROPN
ma-136	744	2	z.	z.	PROPN
ma-136	744	3	li	li	PROPN
ma-136	744	4	,	,	PUNCT
ma-136	744	5	on	on	ADP
ma-136	744	6	the	the	DET
ma-136	744	7	growth	growth	NOUN
ma-136	744	8	of	of	ADP
ma-136	744	9	the	the	DET
ma-136	744	10	solution	solution	NOUN
ma-136	744	11	of	of	ADP
ma-136	744	12	two	two	NUM
ma-136	744	13	-	-	PUNCT
ma-136	744	14	order	order	NOUN
ma-136	744	15	differential	differential	ADJ
ma-136	744	16	equations	equation	NOUN
ma-136	744	17	in	in	ADP
ma-136	744	18	the	the	DET
ma-136	744	19	unit	unit	NOUN
ma-136	744	20	disc	disc	NOUN
ma-136	744	21	.	.	PUNCT
ma-136	745	1	pure	pure	ADJ
ma-136	745	2	appl	appl	PROPN
ma-136	745	3	.	.	PUNCT
ma-136	745	4	math	math	NOUN
ma-136	745	5	.	.	PUNCT
ma-136	746	1	4	4	NUM
ma-136	746	2	(	(	PUNCT
ma-136	746	3	2002)295–300.[20	2002)295–300.[20	NUM
ma-136	746	4	]	]	PUNCT
ma-136	746	5	j.	j.	PROPN
ma-136	746	6	liu	liu	PROPN
ma-136	746	7	,	,	PUNCT
ma-136	746	8	j.	j.	PROPN
ma-136	746	9	tu	tu	PROPN
ma-136	746	10	and	and	CCONJ
ma-136	746	11	l.	l.	PROPN
ma-136	746	12	z.	z.	PROPN
ma-136	746	13	shi	shi	PROPN
ma-136	746	14	,	,	PUNCT
ma-136	746	15	linear	linear	PROPN
ma-136	746	16	differential	differential	ADJ
ma-136	746	17	equations	equation	NOUN
ma-136	746	18	with	with	ADP
ma-136	746	19	entire	entire	ADJ
ma-136	746	20	coefficients	coefficient	NOUN
ma-136	746	21	of	of	ADP
ma-136	746	22	[	[	X
ma-136	746	23	p	p	X
ma-136	746	24	,	,	PUNCT
ma-136	746	25	q]-order	q]-order	NOUN
ma-136	746	26	in	in	ADP
ma-136	746	27	the	the	DET
ma-136	746	28	complex	complex	ADJ
ma-136	746	29	plane	plane	NOUN
ma-136	746	30	.	.	PUNCT
ma-136	747	1	j.math	j.math	NOUN
ma-136	747	2	.	.	PUNCT
ma-136	748	1	anal	anal	PROPN
ma-136	748	2	.	.	PUNCT
ma-136	748	3	appl	appl	PROPN
ma-136	748	4	.	.	PUNCT
ma-136	749	1	372	372	NUM
ma-136	749	2	(	(	PUNCT
ma-136	749	3	2010	2010	NUM
ma-136	749	4	)	)	PUNCT
ma-136	749	5	55–67	55–67	NUM
ma-136	749	6	.	.	PUNCT
ma-136	750	1	https://doi.org/10.1016/j.jmaa.2010.05.014.[21	https://doi.org/10.1016/j.jmaa.2010.05.014.[21	NOUN
ma-136	750	2	]	]	PUNCT
ma-136	751	1	m.	m.	PROPN
ma-136	751	2	tsuji	tsuji	PROPN
ma-136	751	3	,	,	PUNCT
ma-136	751	4	potential	potential	ADJ
ma-136	751	5	theory	theory	NOUN
ma-136	751	6	in	in	ADP
ma-136	751	7	modern	modern	ADJ
ma-136	751	8	function	function	NOUN
ma-136	751	9	theory	theory	NOUN
ma-136	751	10	.	.	PUNCT
ma-136	752	1	chelsea	chelsea	PROPN
ma-136	752	2	,	,	PUNCT
ma-136	752	3	new	new	PROPN
ma-136	752	4	york	york	PROPN
ma-136	752	5	,	,	PUNCT
ma-136	752	6	(	(	PUNCT
ma-136	752	7	1975	1975	NUM
ma-136	752	8	)	)	PUNCT
ma-136	752	9	,	,	PUNCT
ma-136	752	10	reprint	reprint	NOUN
ma-136	752	11	of	of	ADP
ma-136	752	12	the	the	DET
ma-136	752	13	1959	1959	NUM
ma-136	752	14	edition.[22	edition.[22	PROPN
ma-136	752	15	]	]	PUNCT
ma-136	752	16	j.	j.	PROPN
ma-136	752	17	tu	tu	PROPN
ma-136	752	18	and	and	CCONJ
ma-136	752	19	z.	z.	PROPN
ma-136	752	20	x.	x.	PROPN
ma-136	752	21	xuan	xuan	PROPN
ma-136	752	22	,	,	PUNCT
ma-136	752	23	complex	complex	ADJ
ma-136	752	24	linear	linear	ADJ
ma-136	752	25	differential	differential	NOUN
ma-136	752	26	equations	equation	NOUN
ma-136	752	27	with	with	ADP
ma-136	752	28	certain	certain	ADJ
ma-136	752	29	analytic	analytic	ADJ
ma-136	752	30	coefficients	coefficient	NOUN
ma-136	752	31	of	of	ADP
ma-136	752	32	[	[	X
ma-136	752	33	p	p	X
ma-136	752	34	,	,	PUNCT
ma-136	752	35	q]-order	q]-order	NOUN
ma-136	752	36	in	in	ADP
ma-136	752	37	the	the	DET
ma-136	752	38	unitdisc	unitdisc	NOUN
ma-136	752	39	.	.	PUNCT
ma-136	753	1	adv	adv	PROPN
ma-136	753	2	.	.	PUNCT
ma-136	754	1	diff	diff	PROPN
ma-136	754	2	.	.	PUNCT
ma-136	755	1	equ	equ	PROPN
ma-136	755	2	.	.	PROPN
ma-136	755	3	2014	2014	NUM
ma-136	755	4	(	(	PUNCT
ma-136	755	5	2014	2014	NUM
ma-136	755	6	)	)	PUNCT
ma-136	755	7	167	167	NUM
ma-136	755	8	.	.	PUNCT
ma-136	756	1	https://doi.org/10.1186/1687-1847-2014-167	https://doi.org/10.1186/1687-1847-2014-167	ADJ
ma-136	756	2	.	.	PUNCT
ma-136	757	1	https://doi.org/10.28924/ada/ma.3.10	https://doi.org/10.28924/ada/ma.3.10	ADV
ma-136	757	2	http://doi.org/10.5644/sjm.09.1.06	http://doi.org/10.5644/sjm.09.1.06	ADV
ma-136	757	3	https://doi.org/10.1016/j.jmaa.2010.05.014	https://doi.org/10.1016/j.jmaa.2010.05.014	VERB
ma-136	757	4	https://doi.org/10.1186/1687-1847-2014-167	https://doi.org/10.1186/1687-1847-2014-167	ADJ
ma-136	757	5	1	1	NUM
ma-136	757	6	.	.	PUNCT
ma-136	757	7	introduction	introduction	NOUN
ma-136	757	8	and	and	CCONJ
ma-136	757	9	main	main	ADJ
ma-136	757	10	results	result	NOUN
ma-136	757	11	2	2	NUM
ma-136	757	12	.	.	X
ma-136	758	1	some	some	DET
ma-136	758	2	lemmas	lemmas	ADJ
ma-136	758	3	3	3	NUM
ma-136	758	4	.	.	PUNCT
ma-136	758	5	proofs	proof	NOUN
ma-136	758	6	of	of	ADP
ma-136	758	7	theorems	theorem	NOUN
ma-136	758	8	1.1	1.1	NUM
ma-136	758	9	to	to	PART
ma-136	758	10	1.8	1.8	NUM
ma-136	758	11	4	4	NUM
ma-136	758	12	.	.	PUNCT
ma-136	759	1	proof	proof	NOUN
ma-136	759	2	of	of	ADP
ma-136	759	3	theorem	theorem	ADJ
ma-136	759	4	1.9	1.9	NUM
ma-136	759	5	5	5	NUM
ma-136	759	6	.	.	PUNCT
ma-136	760	1	proofs	proof	NOUN
ma-136	760	2	of	of	ADP
ma-136	760	3	theorem	theorem	ADJ
ma-136	760	4	1.10	1.10	NUM
ma-136	760	5	and	and	CCONJ
ma-136	760	6	1.11	1.11	NUM
ma-136	760	7	6	6	NUM
ma-136	760	8	.	.	PUNCT
ma-136	761	1	examples	example	NOUN
ma-136	761	2	references	reference	NOUN