id	sid	tid	token	lemma	pos
ma-227	1	1	2024	2024	NUM
ma-227	1	2	ada	ada	PROPN
ma-227	1	3	academica	academica	PROPN
ma-227	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-227	1	5	.	.	PUNCT
ma-227	2	1	j.	j.	PROPN
ma-227	2	2	math	math	PROPN
ma-227	2	3	.	.	PUNCT
ma-227	3	1	anal	anal	ADJ
ma-227	3	2	.	.	PUNCT
ma-227	4	1	4	4	NUM
ma-227	4	2	(	(	PUNCT
ma-227	4	3	2024	2024	NUM
ma-227	4	4	)	)	PUNCT
ma-227	4	5	15doi	15doi	NOUN
ma-227	4	6	:	:	PUNCT
ma-227	4	7	10.28924	10.28924	NUM
ma-227	4	8	/	/	SYM
ma-227	4	9	ada	ada	PROPN
ma-227	4	10	/	/	SYM
ma-227	4	11	ma.4.15	ma.4.15	PROPN
ma-227	4	12	on	on	ADP
ma-227	4	13	the	the	DET
ma-227	4	14	dirichlet	dirichlet	PROPN
ma-227	4	15	boundary	boundary	PROPN
ma-227	4	16	value	value	NOUN
ma-227	4	17	problem	problem	NOUN
ma-227	4	18	for	for	ADP
ma-227	4	19	the	the	DET
ma-227	4	20	cauchy	cauchy	PROPN
ma-227	4	21	–	–	PUNCT
ma-227	4	22	riemann	riemann	PROPN
ma-227	4	23	equations	equation	NOUN
ma-227	4	24	in	in	ADP
ma-227	4	25	the	the	DET
ma-227	4	26	half	half	ADJ
ma-227	4	27	disc	disc	NOUN
ma-227	4	28	ali	ali	PROPN
ma-227	4	29	darya1,∗	darya1,∗	PROPN
ma-227	4	30	,	,	PUNCT
ma-227	4	31	nasir	nasir	PROPN
ma-227	4	32	tagizadeh2	tagizadeh2	PROPN
ma-227	5	1	1faculty	1faculty	NUM
ma-227	5	2	of	of	ADP
ma-227	5	3	mathematics	mathematics	PROPN
ma-227	5	4	sciences	sciences	PROPN
ma-227	5	5	,	,	PUNCT
ma-227	5	6	university	university	NOUN
ma-227	5	7	of	of	ADP
ma-227	5	8	guilan	guilan	PROPN
ma-227	5	9	,	,	PUNCT
ma-227	5	10	rasht	rasht	NOUN
ma-227	5	11	,	,	PUNCT
ma-227	5	12	19141	19141	NUM
ma-227	5	13	,	,	PUNCT
ma-227	5	14	iran	iran	PROPN
ma-227	5	15	alidarya@phd.guilan.ac.ir	alidarya@phd.guilan.ac.ir	VERB
ma-227	5	16	2faculty	2faculty	NUM
ma-227	5	17	of	of	ADP
ma-227	5	18	mathematics	mathematics	PROPN
ma-227	5	19	sciences	sciences	PROPN
ma-227	5	20	,	,	PUNCT
ma-227	5	21	university	university	NOUN
ma-227	5	22	of	of	ADP
ma-227	5	23	guilan	guilan	PROPN
ma-227	5	24	,	,	PUNCT
ma-227	5	25	rasht	rasht	NOUN
ma-227	5	26	,	,	PUNCT
ma-227	5	27	19141	19141	NUM
ma-227	5	28	,	,	PUNCT
ma-227	5	29	iran	iran	PROPN
ma-227	5	30	taghizadeh@guilan.ac.ir	taghizadeh@guilan.ac.ir	PROPN
ma-227	5	31	∗correspondence	∗correspondence	NOUN
ma-227	5	32	:	:	PUNCT
ma-227	5	33	alidarya@phd.guilan.ac.ir	alidarya@phd.guilan.ac.ir	PROPN
ma-227	5	34	abstract	abstract	ADJ
ma-227	5	35	.	.	PUNCT
ma-227	6	1	in	in	ADP
ma-227	6	2	this	this	DET
ma-227	6	3	article	article	NOUN
ma-227	6	4	,	,	PUNCT
ma-227	6	5	we	we	PRON
ma-227	6	6	investigate	investigate	VERB
ma-227	6	7	the	the	DET
ma-227	6	8	dirichlet	dirichlet	PROPN
ma-227	6	9	boundary	boundary	PROPN
ma-227	6	10	value	value	NOUN
ma-227	6	11	problem	problem	NOUN
ma-227	6	12	for	for	ADP
ma-227	6	13	the	the	DET
ma-227	6	14	cauchy	cauchy	PROPN
ma-227	6	15	–	–	PUNCT
ma-227	6	16	riemann	riemann	PROPN
ma-227	6	17	equations	equation	NOUN
ma-227	6	18	in	in	ADP
ma-227	6	19	the	the	DET
ma-227	6	20	half	half	ADJ
ma-227	6	21	disc	disc	NOUN
ma-227	6	22	.	.	PUNCT
ma-227	7	1	first	first	ADV
ma-227	7	2	,	,	PUNCT
ma-227	7	3	using	use	VERB
ma-227	7	4	the	the	DET
ma-227	7	5	technique	technique	NOUN
ma-227	7	6	of	of	ADP
ma-227	7	7	parqueting	parquete	VERB
ma-227	7	8	–	–	PUNCT
ma-227	7	9	reflection	reflection	NOUN
ma-227	7	10	and	and	CCONJ
ma-227	7	11	thecauchy	thecauchy	ADJ
ma-227	7	12	–	–	PUNCT
ma-227	7	13	pompeiu	pompeiu	NOUN
ma-227	7	14	representation	representation	NOUN
ma-227	7	15	formula	formula	NOUN
ma-227	7	16	for	for	ADP
ma-227	7	17	a	a	DET
ma-227	7	18	half	half	ADJ
ma-227	7	19	disc	disc	NOUN
ma-227	7	20	,	,	PUNCT
ma-227	7	21	we	we	PRON
ma-227	7	22	obtain	obtain	VERB
ma-227	7	23	an	an	DET
ma-227	7	24	integral	integral	ADJ
ma-227	7	25	representation	representation	NOUN
ma-227	7	26	formulain	formulain	VERB
ma-227	7	27	the	the	DET
ma-227	7	28	half	half	ADJ
ma-227	7	29	disc	disc	NOUN
ma-227	7	30	.	.	PUNCT
ma-227	8	1	in	in	ADP
ma-227	8	2	other	other	ADJ
ma-227	8	3	words	word	NOUN
ma-227	8	4	,	,	PUNCT
ma-227	8	5	we	we	PRON
ma-227	8	6	construct	construct	VERB
ma-227	8	7	a	a	DET
ma-227	8	8	unique	unique	ADJ
ma-227	8	9	solution	solution	NOUN
ma-227	8	10	for	for	ADP
ma-227	8	11	the	the	DET
ma-227	8	12	dirichlet	dirichlet	PROPN
ma-227	8	13	boundary	boundary	PROPN
ma-227	8	14	valueproblem	valueproblem	NOUN
ma-227	8	15	.	.	PUNCT
ma-227	9	1	finally	finally	ADV
ma-227	9	2	,	,	PUNCT
ma-227	9	3	we	we	PRON
ma-227	9	4	solve	solve	VERB
ma-227	9	5	the	the	DET
ma-227	9	6	dirichlet	dirichlet	PROPN
ma-227	9	7	boundary	boundary	PROPN
ma-227	9	8	value	value	NOUN
ma-227	9	9	problem	problem	NOUN
ma-227	9	10	for	for	ADP
ma-227	9	11	both	both	CCONJ
ma-227	9	12	the	the	DET
ma-227	9	13	homogeneous	homogeneous	ADJ
ma-227	9	14	andthe	andthe	ADJ
ma-227	9	15	inhomogeneous	inhomogeneous	ADJ
ma-227	9	16	cauchy	cauchy	PROPN
ma-227	9	17	–	–	PUNCT
ma-227	9	18	riemann	riemann	PROPN
ma-227	9	19	equations	equation	NOUN
ma-227	9	20	.	.	PUNCT
ma-227	10	1	in	in	ADP
ma-227	10	2	particular	particular	ADJ
ma-227	10	3	,	,	PUNCT
ma-227	10	4	the	the	DET
ma-227	10	5	boundary	boundary	ADJ
ma-227	10	6	behaviors	behavior	NOUN
ma-227	10	7	at	at	ADP
ma-227	10	8	the	the	DET
ma-227	10	9	cornerpoints	cornerpoint	NOUN
ma-227	10	10	are	be	AUX
ma-227	10	11	considered	consider	VERB
ma-227	10	12	.	.	PUNCT
ma-227	11	1	1	1	X
ma-227	11	2	.	.	X
ma-227	11	3	introduction	introduction	NOUN
ma-227	11	4	and	and	CCONJ
ma-227	11	5	preliminaries	preliminary	NOUN
ma-227	11	6	boundary	boundary	ADJ
ma-227	11	7	value	value	NOUN
ma-227	11	8	problems	problem	NOUN
ma-227	11	9	are	be	AUX
ma-227	11	10	an	an	DET
ma-227	11	11	essential	essential	ADJ
ma-227	11	12	concept	concept	NOUN
ma-227	11	13	in	in	ADP
ma-227	11	14	the	the	DET
ma-227	11	15	field	field	NOUN
ma-227	11	16	of	of	ADP
ma-227	11	17	mathematical	mathematical	ADJ
ma-227	11	18	analysis	analysis	NOUN
ma-227	11	19	andpartial	andpartial	ADJ
ma-227	11	20	differential	differential	NOUN
ma-227	11	21	equations	equation	NOUN
ma-227	11	22	.	.	PUNCT
ma-227	12	1	they	they	PRON
ma-227	12	2	arise	arise	VERB
ma-227	12	3	when	when	SCONJ
ma-227	12	4	seeking	seek	VERB
ma-227	12	5	solutions	solution	NOUN
ma-227	12	6	partial	partial	ADJ
ma-227	12	7	differential	differential	ADJ
ma-227	12	8	equationssubject	equationssubject	NOUN
ma-227	12	9	to	to	ADP
ma-227	12	10	specific	specific	ADJ
ma-227	12	11	conditions	condition	NOUN
ma-227	12	12	on	on	ADP
ma-227	12	13	different	different	ADJ
ma-227	12	14	parts	part	NOUN
ma-227	12	15	of	of	ADP
ma-227	12	16	the	the	DET
ma-227	12	17	boundary	boundary	NOUN
ma-227	12	18	of	of	ADP
ma-227	12	19	the	the	DET
ma-227	12	20	domain	domain	NOUN
ma-227	12	21	.	.	PUNCT
ma-227	13	1	the	the	DET
ma-227	13	2	dirichletboundary	dirichletboundary	ADJ
ma-227	13	3	value	value	NOUN
ma-227	13	4	problem	problem	NOUN
ma-227	13	5	is	be	AUX
ma-227	13	6	a	a	DET
ma-227	13	7	fundamental	fundamental	ADJ
ma-227	13	8	concept	concept	NOUN
ma-227	13	9	in	in	ADP
ma-227	13	10	mathematical	mathematical	ADJ
ma-227	13	11	analysis	analysis	NOUN
ma-227	13	12	,	,	PUNCT
ma-227	13	13	particularly	particularly	ADV
ma-227	13	14	in	in	ADP
ma-227	13	15	thefield	thefield	NOUN
ma-227	13	16	of	of	ADP
ma-227	13	17	partial	partial	ADJ
ma-227	13	18	differential	differential	ADJ
ma-227	13	19	equations	equation	NOUN
ma-227	13	20	.	.	PUNCT
ma-227	14	1	it	it	PRON
ma-227	14	2	deals	deal	VERB
ma-227	14	3	with	with	ADP
ma-227	14	4	finding	find	VERB
ma-227	14	5	a	a	DET
ma-227	14	6	solution	solution	NOUN
ma-227	14	7	to	to	ADP
ma-227	14	8	a	a	DET
ma-227	14	9	partial	partial	ADJ
ma-227	14	10	differentialequation	differentialequation	NOUN
ma-227	14	11	that	that	PRON
ma-227	14	12	satisfies	satisfy	VERB
ma-227	14	13	certain	certain	ADJ
ma-227	14	14	prescribed	prescribed	ADJ
ma-227	14	15	conditions	condition	NOUN
ma-227	14	16	on	on	ADP
ma-227	14	17	the	the	DET
ma-227	14	18	boundary	boundary	NOUN
ma-227	14	19	of	of	ADP
ma-227	14	20	a	a	DET
ma-227	14	21	given	give	VERB
ma-227	14	22	domain.one	domain.one	X
ma-227	14	23	of	of	ADP
ma-227	14	24	the	the	DET
ma-227	14	25	most	most	ADV
ma-227	14	26	powerful	powerful	ADJ
ma-227	14	27	tools	tool	NOUN
ma-227	14	28	for	for	ADP
ma-227	14	29	constructing	construct	VERB
ma-227	14	30	solutions	solution	NOUN
ma-227	14	31	to	to	ADP
ma-227	14	32	the	the	DET
ma-227	14	33	dirichlet	dirichlet	PROPN
ma-227	14	34	problem	problem	NOUN
ma-227	14	35	is	be	AUX
ma-227	14	36	the	the	DET
ma-227	14	37	integralrepresentation	integralrepresentation	NOUN
ma-227	14	38	formula	formula	NOUN
ma-227	14	39	.	.	PUNCT
ma-227	15	1	it	it	PRON
ma-227	15	2	provides	provide	VERB
ma-227	15	3	a	a	DET
ma-227	15	4	way	way	NOUN
ma-227	15	5	to	to	PART
ma-227	15	6	express	express	VERB
ma-227	15	7	the	the	DET
ma-227	15	8	solution	solution	NOUN
ma-227	15	9	in	in	ADP
ma-227	15	10	term	term	NOUN
ma-227	15	11	of	of	ADP
ma-227	15	12	an	an	DET
ma-227	15	13	integral	integral	ADJ
ma-227	15	14	over	over	ADP
ma-227	15	15	theboundary	theboundary	NOUN
ma-227	15	16	of	of	ADP
ma-227	15	17	domain	domain	NOUN
ma-227	15	18	,	,	PUNCT
ma-227	15	19	which	which	PRON
ma-227	15	20	can	can	AUX
ma-227	15	21	often	often	ADV
ma-227	15	22	simplify	simplify	VERB
ma-227	15	23	the	the	DET
ma-227	15	24	problem	problem	NOUN
ma-227	15	25	and	and	CCONJ
ma-227	15	26	lead	lead	VERB
ma-227	15	27	to	to	ADP
ma-227	15	28	explicit	explicit	ADJ
ma-227	15	29	solutions	solution	NOUN
ma-227	15	30	.	.	PUNCT
ma-227	16	1	this	this	DET
ma-227	16	2	formulaallows	formulaallow	VERB
ma-227	16	3	for	for	ADP
ma-227	16	4	the	the	DET
ma-227	16	5	efficient	efficient	ADJ
ma-227	16	6	and	and	CCONJ
ma-227	16	7	accurate	accurate	ADJ
ma-227	16	8	computation	computation	NOUN
ma-227	16	9	of	of	ADP
ma-227	16	10	solutions	solution	NOUN
ma-227	16	11	wide	wide	ADJ
ma-227	16	12	range	range	NOUN
ma-227	16	13	of	of	ADP
ma-227	16	14	partial	partial	ADJ
ma-227	16	15	differentialequations	differentialequation	NOUN
ma-227	16	16	,	,	PUNCT
ma-227	16	17	making	make	VERB
ma-227	16	18	it	it	PRON
ma-227	16	19	an	an	DET
ma-227	16	20	essential	essential	ADJ
ma-227	16	21	tool	tool	NOUN
ma-227	16	22	in	in	ADP
ma-227	16	23	the	the	DET
ma-227	16	24	field	field	NOUN
ma-227	16	25	of	of	ADP
ma-227	16	26	partial	partial	ADJ
ma-227	16	27	differential	differential	NOUN
ma-227	16	28	equations.the	equations.the	DET
ma-227	16	29	parqueting	parqueting	ADJ
ma-227	16	30	–	–	PUNCT
ma-227	16	31	reflection	reflection	NOUN
ma-227	16	32	principle	principle	NOUN
ma-227	16	33	is	be	AUX
ma-227	16	34	a	a	DET
ma-227	16	35	technique	technique	NOUN
ma-227	16	36	used	use	VERB
ma-227	16	37	in	in	ADP
ma-227	16	38	constructing	construct	VERB
ma-227	16	39	integral	integral	ADJ
ma-227	16	40	representationformulas	representationformula	NOUN
ma-227	16	41	for	for	ADP
ma-227	16	42	the	the	DET
ma-227	16	43	dirichlet	dirichlet	PROPN
ma-227	16	44	boundary	boundary	PROPN
ma-227	16	45	value	value	NOUN
ma-227	16	46	problem	problem	NOUN
ma-227	16	47	.	.	PUNCT
ma-227	17	1	for	for	ADP
ma-227	17	2	specific	specific	ADJ
ma-227	17	3	regions	region	NOUN
ma-227	17	4	of	of	ADP
ma-227	17	5	complex	complex	ADJ
ma-227	17	6	plane	plane	NOUN
ma-227	17	7	whoseboundary	whoseboundary	NOUN
ma-227	17	8	consists	consist	VERB
ma-227	17	9	of	of	ADP
ma-227	17	10	sub	sub	NOUN
ma-227	17	11	-	-	NOUN
ma-227	17	12	arcs	arc	NOUN
ma-227	17	13	of	of	ADP
ma-227	17	14	circles	circle	NOUN
ma-227	17	15	or	or	CCONJ
ma-227	17	16	straight	straight	ADJ
ma-227	17	17	lines	line	NOUN
ma-227	17	18	,	,	PUNCT
ma-227	17	19	the	the	DET
ma-227	17	20	parqueting	parqueting	ADJ
ma-227	17	21	–	–	PUNCT
ma-227	17	22	reflection	reflection	NOUN
ma-227	17	23	method	method	NOUN
ma-227	17	24	for	for	ADP
ma-227	17	25	received	receive	VERB
ma-227	17	26	:	:	PUNCT
ma-227	17	27	13	13	NUM
ma-227	17	28	feb	feb	NOUN
ma-227	17	29	2024	2024	NUM
ma-227	17	30	.	.	PUNCT
ma-227	18	1	key	key	ADJ
ma-227	18	2	words	word	NOUN
ma-227	18	3	and	and	CCONJ
ma-227	18	4	phrases	phrase	NOUN
ma-227	18	5	.	.	PUNCT
ma-227	19	1	cauchy	cauchy	PROPN
ma-227	19	2	–	–	PUNCT
ma-227	19	3	riemann	riemann	PROPN
ma-227	19	4	equation	equation	NOUN
ma-227	19	5	,	,	PUNCT
ma-227	19	6	dirichlet	dirichlet	PROPN
ma-227	19	7	problem	problem	NOUN
ma-227	19	8	,	,	PUNCT
ma-227	19	9	integral	integral	ADJ
ma-227	19	10	representation	representation	NOUN
ma-227	19	11	formula	formula	NOUN
ma-227	19	12	,	,	PUNCT
ma-227	19	13	half	half	NOUN
ma-227	19	14	disc.1	disc.1	VERB
ma-227	19	15	https://adac.ee	https://adac.ee	PROPN
ma-227	19	16	https://doi.org/10.28924/ada/ma.4.15	https://doi.org/10.28924/ada/ma.4.15	PROPN
ma-227	19	17	https://orcid.org/0009-0009-7723-9718	https://orcid.org/0009-0009-7723-9718	PROPN
ma-227	19	18	https://orcid.org/0000-0002-3865-7943	https://orcid.org/0000-0002-3865-7943	PROPN
ma-227	19	19	eur	eur	PROPN
ma-227	19	20	.	.	PUNCT
ma-227	20	1	j.	j.	PROPN
ma-227	20	2	math	math	PROPN
ma-227	20	3	.	.	PUNCT
ma-227	21	1	anal	anal	PROPN
ma-227	21	2	.	.	PUNCT
ma-227	22	1	10.28924	10.28924	NUM
ma-227	22	2	/	/	SYM
ma-227	22	3	ada	ada	PROPN
ma-227	22	4	/	/	SYM
ma-227	22	5	ma.4.15	ma.4.15	NOUN
ma-227	22	6	2constructing	2constructing	NUM
ma-227	22	7	integral	integral	ADJ
ma-227	22	8	representation	representation	NOUN
ma-227	22	9	formula	formula	NOUN
ma-227	22	10	to	to	PART
ma-227	22	11	solve	solve	VERB
ma-227	22	12	the	the	DET
ma-227	22	13	dirichlet	dirichlet	PROPN
ma-227	22	14	boundary	boundary	PROPN
ma-227	22	15	value	value	NOUN
ma-227	22	16	problem	problem	NOUN
ma-227	22	17	for	for	ADP
ma-227	22	18	thecauchy	thecauchy	NOUN
ma-227	22	19	–	–	PUNCT
ma-227	22	20	riemann	riemann	PROPN
ma-227	22	21	equation	equation	NOUN
ma-227	22	22	is	be	AUX
ma-227	22	23	used	use	VERB
ma-227	22	24	.	.	PUNCT
ma-227	23	1	if	if	SCONJ
ma-227	23	2	the	the	DET
ma-227	23	3	boundary	boundary	NOUN
ma-227	23	4	of	of	ADP
ma-227	23	5	the	the	DET
ma-227	23	6	region	region	NOUN
ma-227	23	7	has	have	VERB
ma-227	23	8	the	the	DET
ma-227	23	9	mentioned	mention	VERB
ma-227	23	10	characteristics	characteristic	NOUN
ma-227	23	11	,	,	PUNCT
ma-227	23	12	it	it	PRON
ma-227	23	13	is	be	AUX
ma-227	23	14	possible	possible	ADJ
ma-227	23	15	to	to	PART
ma-227	23	16	create	create	VERB
ma-227	23	17	a	a	DET
ma-227	23	18	new	new	ADJ
ma-227	23	19	region	region	NOUN
ma-227	23	20	by	by	ADP
ma-227	23	21	reflecting	reflect	VERB
ma-227	23	22	the	the	DET
ma-227	23	23	main	main	ADJ
ma-227	23	24	region	region	NOUN
ma-227	23	25	with	with	ADP
ma-227	23	26	respect	respect	NOUN
ma-227	23	27	to	to	ADP
ma-227	23	28	its	its	PRON
ma-227	23	29	boundaryand	boundaryand	NOUN
ma-227	23	30	by	by	ADP
ma-227	23	31	reflecting	reflect	VERB
ma-227	23	32	this	this	DET
ma-227	23	33	new	new	ADJ
ma-227	23	34	region	region	NOUN
ma-227	23	35	with	with	ADP
ma-227	23	36	respect	respect	NOUN
ma-227	23	37	to	to	ADP
ma-227	23	38	its	its	PRON
ma-227	23	39	boundary	boundary	NOUN
ma-227	23	40	,	,	PUNCT
ma-227	23	41	another	another	DET
ma-227	23	42	region	region	NOUN
ma-227	23	43	is	be	AUX
ma-227	23	44	obtained	obtain	VERB
ma-227	23	45	.	.	PUNCT
ma-227	24	1	bycontinuing	bycontinue	VERB
ma-227	24	2	this	this	DET
ma-227	24	3	process	process	NOUN
ma-227	24	4	,	,	PUNCT
ma-227	24	5	we	we	PRON
ma-227	24	6	reach	reach	VERB
ma-227	24	7	pieces	piece	NOUN
ma-227	24	8	of	of	ADP
ma-227	24	9	the	the	DET
ma-227	24	10	plane	plane	NOUN
ma-227	24	11	that	that	PRON
ma-227	24	12	the	the	DET
ma-227	24	13	union	union	NOUN
ma-227	24	14	of	of	ADP
ma-227	24	15	these	these	DET
ma-227	24	16	pieces	piece	NOUN
ma-227	24	17	provides	provide	VERB
ma-227	24	18	acover	acover	ADV
ma-227	24	19	for	for	ADP
ma-227	24	20	the	the	DET
ma-227	24	21	complex	complex	ADJ
ma-227	24	22	plane	plane	NOUN
ma-227	24	23	.	.	PUNCT
ma-227	25	1	this	this	DET
ma-227	25	2	cover	cover	NOUN
ma-227	25	3	can	can	AUX
ma-227	25	4	be	be	AUX
ma-227	25	5	achieved	achieve	VERB
ma-227	25	6	through	through	ADP
ma-227	25	7	a	a	DET
ma-227	25	8	single	single	ADJ
ma-227	25	9	reflection	reflection	NOUN
ma-227	25	10	or	or	CCONJ
ma-227	25	11	multipleconsecutive	multipleconsecutive	ADJ
ma-227	25	12	reflections	reflection	NOUN
ma-227	25	13	or	or	CCONJ
ma-227	25	14	infinite	infinite	VERB
ma-227	25	15	repetitive	repetitive	ADJ
ma-227	25	16	reflections	reflection	NOUN
ma-227	25	17	.	.	PUNCT
ma-227	26	1	therefore	therefore	ADV
ma-227	26	2	,	,	PUNCT
ma-227	26	3	the	the	DET
ma-227	26	4	reflection	reflection	NOUN
ma-227	26	5	of	of	ADP
ma-227	26	6	the	the	DET
ma-227	26	7	main	main	ADJ
ma-227	26	8	regionat	regionat	NOUN
ma-227	26	9	its	its	PRON
ma-227	26	10	boundary	boundary	NOUN
ma-227	26	11	is	be	AUX
ma-227	26	12	repeated	repeat	VERB
ma-227	26	13	to	to	PART
ma-227	26	14	achieve	achieve	VERB
ma-227	26	15	a	a	DET
ma-227	26	16	cover	cover	NOUN
ma-227	26	17	for	for	SCONJ
ma-227	26	18	complex	complex	ADJ
ma-227	26	19	plane.many	plane.many	PROPN
ma-227	26	20	results	result	NOUN
ma-227	26	21	have	have	AUX
ma-227	26	22	been	be	AUX
ma-227	26	23	obtained	obtain	VERB
ma-227	26	24	for	for	ADP
ma-227	26	25	boundary	boundary	ADJ
ma-227	26	26	value	value	NOUN
ma-227	26	27	problems	problem	NOUN
ma-227	26	28	of	of	ADP
ma-227	26	29	complex	complex	ADJ
ma-227	26	30	partial	partial	ADJ
ma-227	26	31	differentialequations	differentialequation	NOUN
ma-227	26	32	in	in	ADP
ma-227	26	33	some	some	DET
ma-227	26	34	particular	particular	ADJ
ma-227	26	35	domains	domain	NOUN
ma-227	26	36	,	,	PUNCT
ma-227	26	37	see	see	VERB
ma-227	26	38	,	,	PUNCT
ma-227	27	1	e.g.	e.g.	ADV
ma-227	27	2	[	[	X
ma-227	27	3	1–16	1–16	NOUN
ma-227	27	4	]	]	PUNCT
ma-227	27	5	.	.	PUNCT
ma-227	28	1	in	in	ADP
ma-227	28	2	the	the	DET
ma-227	28	3	year	year	NOUN
ma-227	28	4	2009	2009	NUM
ma-227	28	5	,	,	PUNCT
ma-227	28	6	harmonic	harmonic	ADJ
ma-227	28	7	boundary	boundary	ADJ
ma-227	28	8	valueproblem	valueproblem	NOUN
ma-227	28	9	for	for	ADP
ma-227	28	10	the	the	DET
ma-227	28	11	poisson	poisson	NOUN
ma-227	28	12	equation	equation	NOUN
ma-227	28	13	in	in	ADP
ma-227	28	14	a	a	DET
ma-227	28	15	half	half	ADJ
ma-227	28	16	disc	disc	NOUN
ma-227	28	17	was	be	AUX
ma-227	28	18	presented	present	VERB
ma-227	28	19	by	by	ADP
ma-227	28	20	h.	h.	PROPN
ma-227	28	21	begehr	begehr	PROPN
ma-227	28	22	and	and	CCONJ
ma-227	28	23	t.	t.	PROPN
ma-227	28	24	vaitekhovich	vaitekhovich	PROPN
ma-227	29	1	[	[	X
ma-227	29	2	2].in	2].in	NUM
ma-227	29	3	2012	2012	NUM
ma-227	29	4	,	,	PUNCT
ma-227	29	5	y.	y.	PROPN
ma-227	29	6	wang	wang	PROPN
ma-227	29	7	introduced	introduce	VERB
ma-227	29	8	schwarz	schwarz	ADJ
ma-227	29	9	-	-	PUNCT
ma-227	29	10	type	type	NOUN
ma-227	29	11	boundary	boundary	ADJ
ma-227	29	12	value	value	NOUN
ma-227	29	13	problems	problem	NOUN
ma-227	29	14	for	for	ADP
ma-227	29	15	the	the	DET
ma-227	29	16	polyanalytic	polyanalytic	ADJ
ma-227	29	17	equationin	equationin	NOUN
ma-227	29	18	the	the	DET
ma-227	29	19	half	half	ADJ
ma-227	29	20	unit	unit	NOUN
ma-227	29	21	disc	disc	VERB
ma-227	29	22	[	[	X
ma-227	29	23	16].in	16].in	NUM
ma-227	29	24	this	this	DET
ma-227	29	25	article	article	NOUN
ma-227	29	26	,	,	PUNCT
ma-227	29	27	in	in	ADP
ma-227	29	28	addition	addition	NOUN
ma-227	29	29	to	to	ADP
ma-227	29	30	introducing	introduce	VERB
ma-227	29	31	the	the	DET
ma-227	29	32	domain	domain	NOUN
ma-227	29	33	of	of	ADP
ma-227	29	34	half	half	ADJ
ma-227	29	35	disc	disc	NOUN
ma-227	29	36	,	,	PUNCT
ma-227	29	37	we	we	PRON
ma-227	29	38	want	want	VERB
ma-227	29	39	to	to	PART
ma-227	29	40	express	express	VERB
ma-227	29	41	the	the	DET
ma-227	29	42	reflections	reflection	NOUN
ma-227	29	43	,	,	PUNCT
ma-227	29	44	covering	covering	NOUN
ma-227	29	45	and	and	CCONJ
ma-227	29	46	points	point	NOUN
ma-227	29	47	that	that	SCONJ
ma-227	29	48	we	we	PRON
ma-227	29	49	obtain	obtain	VERB
ma-227	29	50	at	at	ADP
ma-227	29	51	each	each	DET
ma-227	29	52	stage	stage	NOUN
ma-227	29	53	.	.	PUNCT
ma-227	30	1	we	we	PRON
ma-227	30	2	also	also	ADV
ma-227	30	3	construct	construct	VERB
ma-227	30	4	the	the	DET
ma-227	30	5	integral	integral	ADJ
ma-227	30	6	representationformula	representationformula	NOUN
ma-227	30	7	using	use	VERB
ma-227	30	8	the	the	DET
ma-227	30	9	parqueting	parqueting	ADJ
ma-227	30	10	–	–	PUNCT
ma-227	30	11	reflection	reflection	NOUN
ma-227	30	12	method	method	NOUN
ma-227	30	13	and	and	CCONJ
ma-227	30	14	investigate	investigate	VERB
ma-227	30	15	the	the	DET
ma-227	30	16	dirichlet	dirichlet	PROPN
ma-227	30	17	problem	problem	NOUN
ma-227	30	18	.	.	PUNCT
ma-227	31	1	in	in	ADP
ma-227	31	2	particular	particular	ADJ
ma-227	31	3	,	,	PUNCT
ma-227	31	4	we	we	PRON
ma-227	31	5	study	study	VERB
ma-227	31	6	the	the	DET
ma-227	31	7	explicit	explicit	ADJ
ma-227	31	8	solvability	solvability	NOUN
ma-227	31	9	of	of	ADP
ma-227	31	10	the	the	DET
ma-227	31	11	dirichlet	dirichlet	PROPN
ma-227	31	12	boundary	boundary	PROPN
ma-227	31	13	value	value	NOUN
ma-227	31	14	problem	problem	NOUN
ma-227	31	15	for	for	ADP
ma-227	31	16	both	both	CCONJ
ma-227	31	17	the	the	DET
ma-227	31	18	homogeneousand	homogeneousand	NOUN
ma-227	31	19	the	the	DET
ma-227	31	20	inhomogeneous	inhomogeneous	ADJ
ma-227	31	21	cauchy	cauchy	PROPN
ma-227	31	22	–	–	PUNCT
ma-227	31	23	riemann	riemann	PROPN
ma-227	31	24	equations	equation	NOUN
ma-227	31	25	in	in	ADP
ma-227	31	26	the	the	DET
ma-227	31	27	half	half	NOUN
ma-227	31	28	disc.in	disc.in	PRON
ma-227	31	29	this	this	DET
ma-227	31	30	article	article	NOUN
ma-227	31	31	,	,	PUNCT
ma-227	31	32	let	let	VERB
ma-227	31	33	m	m	PRON
ma-227	31	34	be	be	AUX
ma-227	31	35	the	the	DET
ma-227	31	36	half	half	ADJ
ma-227	31	37	disc	disc	NOUN
ma-227	31	38	domain	domain	NOUN
ma-227	31	39	in	in	ADP
ma-227	31	40	the	the	DET
ma-227	31	41	complex	complex	ADJ
ma-227	31	42	plane	plane	NOUN
ma-227	31	43	c	c	NOUN
ma-227	31	44	defined	define	VERB
ma-227	31	45	by	by	ADP
ma-227	31	46	m	m	PROPN
ma-227	31	47	=	=	SYM
ma-227	31	48	{	{	PUNCT
ma-227	31	49	z	z	NOUN
ma-227	31	50	∈	∈	PROPN
ma-227	32	1	c	c	NOUN
ma-227	32	2	:	:	PUNCT
ma-227	32	3	|z	|z	PROPN
ma-227	33	1	|	|	ADV
ma-227	33	2	<	<	X
ma-227	33	3	1	1	NUM
ma-227	33	4	,	,	PUNCT
ma-227	33	5	imz	imz	PROPN
ma-227	33	6	>	>	X
ma-227	33	7	0	0	NUM
ma-227	33	8	}	}	PUNCT
ma-227	33	9	where	where	SCONJ
ma-227	33	10	d	d	NOUN
ma-227	33	11	=	=	PRON
ma-227	33	12	{	{	PUNCT
ma-227	33	13	z	z	NOUN
ma-227	33	14	∈	∈	PROPN
ma-227	33	15	c	c	NOUN
ma-227	33	16	:	:	PUNCT
ma-227	33	17	|z	|z	PROPN
ma-227	34	1	|	|	ADV
ma-227	34	2	=	=	SYM
ma-227	34	3	1	1	X
ma-227	34	4	}	}	PUNCT
ma-227	34	5	and	and	CCONJ
ma-227	34	6	the	the	DET
ma-227	34	7	boundary	boundary	NOUN
ma-227	34	8	of	of	ADP
ma-227	34	9	m	m	PROPN
ma-227	34	10	is	be	AUX
ma-227	34	11	denoted	denote	VERB
ma-227	34	12	by	by	ADP
ma-227	34	13	∂m	∂m	PROPN
ma-227	34	14	.	.	PUNCT
ma-227	35	1	it	it	PRON
ma-227	35	2	is	be	AUX
ma-227	35	3	formed	form	VERB
ma-227	35	4	by	by	ADP
ma-227	35	5	arc	arc	NOUN
ma-227	35	6	of	of	ADP
ma-227	35	7	thecircle	thecircle	NOUN
ma-227	35	8	d	d	NOUN
ma-227	35	9	and	and	CCONJ
ma-227	35	10	a	a	DET
ma-227	35	11	line	line	NOUN
ma-227	35	12	segment	segment	NOUN
ma-227	35	13	on	on	ADP
ma-227	35	14	the	the	DET
ma-227	35	15	real	real	ADJ
ma-227	35	16	axis	axis	NOUN
ma-227	35	17	from	from	ADP
ma-227	35	18	point	point	NOUN
ma-227	35	19	−1	−1	NOUN
ma-227	35	20	to	to	ADP
ma-227	35	21	1	1	NUM
ma-227	35	22	.	.	PUNCT
ma-227	36	1	see	see	VERB
ma-227	36	2	figure	figure	NOUN
ma-227	36	3	1	1	NUM
ma-227	36	4	.	.	PUNCT
ma-227	36	5	figure	figure	NOUN
ma-227	36	6	1	1	NUM
ma-227	36	7	.	.	NOUN
ma-227	36	8	half	half	NOUN
ma-227	36	9	disc	disc	NOUN
ma-227	36	10	m	m	PROPN
ma-227	36	11	https://doi.org/10.28924/ada/ma.4.15	https://doi.org/10.28924/ada/ma.4.15	NOUN
ma-227	36	12	eur	eur	PROPN
ma-227	36	13	.	.	PUNCT
ma-227	37	1	j.	j.	PROPN
ma-227	37	2	math	math	PROPN
ma-227	37	3	.	.	PUNCT
ma-227	38	1	anal	anal	PROPN
ma-227	38	2	.	.	PUNCT
ma-227	39	1	10.28924	10.28924	NUM
ma-227	39	2	/	/	SYM
ma-227	39	3	ada	ada	PROPN
ma-227	39	4	/	/	SYM
ma-227	39	5	ma.4.15	ma.4.15	PROPN
ma-227	39	6	3now	3now	ADV
ma-227	39	7	,	,	PUNCT
ma-227	39	8	we	we	PRON
ma-227	39	9	introduce	introduce	VERB
ma-227	39	10	some	some	DET
ma-227	39	11	important	important	ADJ
ma-227	39	12	definitions	definition	NOUN
ma-227	39	13	and	and	CCONJ
ma-227	39	14	properties	property	NOUN
ma-227	39	15	of	of	ADP
ma-227	39	16	complex	complex	ADJ
ma-227	39	17	analytic	analytic	ADJ
ma-227	39	18	functions	function	NOUN
ma-227	39	19	,	,	PUNCT
ma-227	39	20	re	re	NOUN
ma-227	39	21	-	-	NOUN
ma-227	39	22	sults	sult	NOUN
ma-227	39	23	which	which	PRON
ma-227	39	24	will	will	AUX
ma-227	39	25	be	be	AUX
ma-227	39	26	required	require	VERB
ma-227	39	27	in	in	ADP
ma-227	39	28	subsequent	subsequent	ADJ
ma-227	39	29	sections	section	NOUN
ma-227	39	30	.	.	PUNCT
ma-227	40	1	defining	define	VERB
ma-227	40	2	the	the	DET
ma-227	40	3	complex	complex	ADJ
ma-227	40	4	partial	partial	ADJ
ma-227	40	5	differential	differential	NOUN
ma-227	40	6	operators	operator	NOUN
ma-227	40	7	∂	∂	NUM
ma-227	40	8	∂z	∂z	PROPN
ma-227	40	9	and	and	CCONJ
ma-227	40	10	∂	∂	NUM
ma-227	40	11	∂z̄	∂z̄	NOUN
ma-227	40	12	by	by	ADP
ma-227	40	13	∂	∂	NOUN
ma-227	40	14	∂z	∂z	PROPN
ma-227	40	15	=	=	NOUN
ma-227	40	16	1	1	NUM
ma-227	40	17	2	2	NUM
ma-227	40	18	(	(	PUNCT
ma-227	40	19	∂	∂	NOUN
ma-227	40	20	∂x	∂x	PROPN
ma-227	40	21	−	−	NOUN
ma-227	41	1	i	i	PRON
ma-227	41	2	∂	∂	NOUN
ma-227	41	3	∂y	∂y	NUM
ma-227	41	4	)	)	PUNCT
ma-227	41	5	,	,	PUNCT
ma-227	41	6	∂	∂	NUM
ma-227	41	7	∂z̄	∂z̄	NOUN
ma-227	41	8	=	=	SYM
ma-227	41	9	1	1	NUM
ma-227	41	10	2	2	NUM
ma-227	41	11	(	(	PUNCT
ma-227	41	12	∂	∂	NOUN
ma-227	41	13	∂x	∂x	NOUN
ma-227	42	1	+	+	CCONJ
ma-227	42	2	i	i	PRON
ma-227	42	3	∂	∂	NOUN
ma-227	42	4	∂y	∂y	X
ma-227	42	5	)	)	PUNCT
ma-227	42	6	.	.	PUNCT
ma-227	43	1	let	let	VERB
ma-227	43	2	the	the	DET
ma-227	43	3	complex	complex	ADV
ma-227	43	4	-	-	PUNCT
ma-227	43	5	valued	value	VERB
ma-227	43	6	function	function	NOUN
ma-227	43	7	ω	ω	NOUN
ma-227	43	8	be	be	AUX
ma-227	43	9	defined	define	VERB
ma-227	43	10	in	in	ADP
ma-227	43	11	m	m	PRON
ma-227	43	12	and	and	CCONJ
ma-227	43	13	let	let	VERB
ma-227	43	14	u	u	PRON
ma-227	43	15	and	and	CCONJ
ma-227	43	16	v	v	NOUN
ma-227	43	17	denote	denote	VERB
ma-227	43	18	its	its	PRON
ma-227	43	19	real	real	ADJ
ma-227	43	20	and	and	CCONJ
ma-227	43	21	imaginaryparts	imaginarypart	NOUN
ma-227	43	22	:	:	PUNCT
ma-227	43	23	ω	ω	NUM
ma-227	43	24	=	=	SYM
ma-227	43	25	u+	u+	NUM
ma-227	43	26	iv	iv	NUM
ma-227	43	27	,	,	PUNCT
ma-227	43	28	where	where	SCONJ
ma-227	43	29	u(x	u(x	NOUN
ma-227	43	30	,	,	PUNCT
ma-227	43	31	y	y	NOUN
ma-227	43	32	)	)	PUNCT
ma-227	43	33	and	and	CCONJ
ma-227	43	34	v(x	v(x	PROPN
ma-227	43	35	,	,	PUNCT
ma-227	43	36	y	y	NOUN
ma-227	43	37	)	)	PUNCT
ma-227	43	38	are	be	AUX
ma-227	43	39	real	real	ADV
ma-227	43	40	-	-	PUNCT
ma-227	43	41	valued	value	VERB
ma-227	43	42	functions	function	NOUN
ma-227	43	43	.	.	PUNCT
ma-227	44	1	the	the	DET
ma-227	44	2	two	two	NUM
ma-227	44	3	partial	partial	ADJ
ma-227	44	4	differentialequations	differentialequation	NOUN
ma-227	44	5	∂u	∂u	PROPN
ma-227	44	6	∂x	∂x	PROPN
ma-227	44	7	=	=	SYM
ma-227	44	8	∂v	∂v	PROPN
ma-227	44	9	∂y	∂y	PROPN
ma-227	44	10	,	,	PUNCT
ma-227	44	11	(	(	PUNCT
ma-227	44	12	1.1	1.1	NUM
ma-227	44	13	)	)	PUNCT
ma-227	45	1	∂u	∂u	PROPN
ma-227	45	2	∂y	∂y	X
ma-227	45	3	=	=	PUNCT
ma-227	45	4	−	−	PROPN
ma-227	45	5	∂v	∂v	PROPN
ma-227	45	6	∂x	∂x	PROPN
ma-227	45	7	,	,	PUNCT
ma-227	45	8	(	(	PUNCT
ma-227	45	9	1.2	1.2	NUM
ma-227	45	10	)	)	PUNCT
ma-227	45	11	are	be	AUX
ma-227	45	12	called	call	VERB
ma-227	45	13	the	the	DET
ma-227	45	14	cauchy	cauchy	PROPN
ma-227	45	15	–	–	PUNCT
ma-227	45	16	riemann	riemann	PROPN
ma-227	45	17	equations	equation	NOUN
ma-227	45	18	for	for	ADP
ma-227	45	19	the	the	DET
ma-227	45	20	pair	pair	NOUN
ma-227	45	21	of	of	ADP
ma-227	45	22	functions	function	NOUN
ma-227	45	23	u	u	NOUN
ma-227	45	24	and	and	CCONJ
ma-227	45	25	v	v	NOUN
ma-227	45	26	.	.	PUNCT
ma-227	46	1	multiplying	multiply	VERB
ma-227	46	2	the	the	DET
ma-227	46	3	bothsides	bothside	NOUN
ma-227	46	4	of	of	ADP
ma-227	46	5	the	the	DET
ma-227	46	6	equality	equality	NOUN
ma-227	46	7	(	(	PUNCT
ma-227	46	8	1.2	1.2	NUM
ma-227	46	9	)	)	PUNCT
ma-227	46	10	by	by	ADP
ma-227	46	11	i	i	PRON
ma-227	46	12	,	,	PUNCT
ma-227	46	13	i	i	PRON
ma-227	46	14	(	(	PUNCT
ma-227	47	1	∂u	∂u	PROPN
ma-227	47	2	∂y	∂y	PROPN
ma-227	47	3	+	+	CCONJ
ma-227	47	4	∂v	∂v	PROPN
ma-227	47	5	∂x	∂x	PROPN
ma-227	47	6	)	)	PUNCT
ma-227	48	1	=	=	PUNCT
ma-227	48	2	0	0	X
ma-227	48	3	.	.	PUNCT
ma-227	49	1	(	(	PUNCT
ma-227	49	2	1.3)adding	1.3)adding	NUM
ma-227	49	3	(	(	PUNCT
ma-227	49	4	1.1	1.1	NUM
ma-227	49	5	)	)	PUNCT
ma-227	49	6	and	and	CCONJ
ma-227	49	7	(	(	PUNCT
ma-227	49	8	1.3	1.3	NUM
ma-227	49	9	)	)	PUNCT
ma-227	49	10	leads	lead	VERB
ma-227	49	11	to	to	ADP
ma-227	49	12	∂	∂	ADJ
ma-227	49	13	∂x	∂x	PROPN
ma-227	49	14	(	(	PUNCT
ma-227	49	15	u	u	NOUN
ma-227	49	16	+	+	NOUN
ma-227	49	17	iv	iv	NUM
ma-227	49	18	)	)	PUNCT
ma-227	50	1	+	+	CCONJ
ma-227	50	2	i	i	PRON
ma-227	50	3	∂	∂	ADV
ma-227	50	4	∂y	∂y	X
ma-227	50	5	(	(	PUNCT
ma-227	50	6	u	u	NOUN
ma-227	50	7	−	−	PROPN
ma-227	50	8	1	1	NUM
ma-227	50	9	i	i	NOUN
ma-227	50	10	v	v	NOUN
ma-227	50	11	)	)	PUNCT
ma-227	50	12	=	=	SYM
ma-227	51	1	0	0	X
ma-227	51	2	.	.	PUNCT
ma-227	52	1	thus	thus	ADV
ma-227	52	2	1	1	NUM
ma-227	52	3	2	2	NUM
ma-227	52	4	(	(	PUNCT
ma-227	52	5	∂w	∂w	PROPN
ma-227	52	6	∂x	∂x	PROPN
ma-227	52	7	+	+	CCONJ
ma-227	53	1	i	i	PRON
ma-227	53	2	∂w	∂w	PROPN
ma-227	53	3	∂y	∂y	NOUN
ma-227	53	4	)	)	PUNCT
ma-227	54	1	=	=	PUNCT
ma-227	54	2	0	0	X
ma-227	54	3	.	.	PUNCT
ma-227	55	1	the	the	DET
ma-227	55	2	cauchy	cauchy	PROPN
ma-227	55	3	–	–	PUNCT
ma-227	55	4	riemann	riemann	PROPN
ma-227	55	5	equation	equation	NOUN
ma-227	55	6	can	can	AUX
ma-227	55	7	be	be	AUX
ma-227	55	8	written	write	VERB
ma-227	55	9	as	as	ADP
ma-227	55	10	∂ω	∂ω	ADJ
ma-227	55	11	∂z̄	∂z̄	NOUN
ma-227	55	12	=	=	PUNCT
ma-227	55	13	ωz̄	ωz̄	NOUN
ma-227	56	1	=	=	PUNCT
ma-227	56	2	0	0	PUNCT
ma-227	57	1	and	and	CCONJ
ma-227	57	2	this	this	PRON
ma-227	57	3	is	be	AUX
ma-227	57	4	the	the	DET
ma-227	57	5	condition	condition	NOUN
ma-227	57	6	for	for	ADP
ma-227	57	7	ωto	ωto	ADJ
ma-227	57	8	be	be	AUX
ma-227	57	9	analytic	analytic	ADJ
ma-227	57	10	function	function	NOUN
ma-227	57	11	.	.	PUNCT
ma-227	58	1	recall	recall	VERB
ma-227	58	2	the	the	DET
ma-227	58	3	definition	definition	NOUN
ma-227	58	4	of	of	ADP
ma-227	58	5	the	the	DET
ma-227	58	6	pompeiu	pompeiu	NOUN
ma-227	58	7	integral	integral	ADJ
ma-227	58	8	operator	operator	NOUN
ma-227	58	9	t	t	PROPN
ma-227	58	10	f	f	PROPN
ma-227	58	11	(	(	PUNCT
ma-227	58	12	z	z	NOUN
ma-227	58	13	)	)	PUNCT
ma-227	58	14	=	=	SYM
ma-227	59	1	−	−	PROPN
ma-227	60	1	1	1	NUM
ma-227	60	2	π	π	NOUN
ma-227	60	3	∫	∫	PROPN
ma-227	60	4	m	m	PROPN
ma-227	60	5	f	f	PROPN
ma-227	60	6	(	(	PUNCT
ma-227	60	7	t	t	PROPN
ma-227	60	8	)	)	PUNCT
ma-227	60	9	t	t	NOUN
ma-227	60	10	−	−	PROPN
ma-227	60	11	z	z	PROPN
ma-227	60	12	dξdη	dξdη	PROPN
ma-227	60	13	,	,	PUNCT
ma-227	60	14	t	t	PROPN
ma-227	60	15	f	f	PROPN
ma-227	60	16	(	(	PUNCT
ma-227	60	17	z	z	NOUN
ma-227	60	18	)	)	PUNCT
ma-227	60	19	is	be	AUX
ma-227	60	20	weakly	weakly	ADV
ma-227	60	21	differentiable	differentiable	ADJ
ma-227	60	22	with	with	ADP
ma-227	60	23	ωz̄	ωz̄	NOUN
ma-227	60	24	=	=	PUNCT
ma-227	60	25	f	f	PROPN
ma-227	60	26	when	when	SCONJ
ma-227	60	27	f	f	PROPN
ma-227	60	28	∈	∈	PROPN
ma-227	60	29	lp(m;c	lp(m;c	NOUN
ma-227	60	30	)	)	PUNCT
ma-227	60	31	,	,	PUNCT
ma-227	60	32	p	p	X
ma-227	60	33	>	>	X
ma-227	60	34	2	2	NUM
ma-227	60	35	and	and	CCONJ
ma-227	60	36	t	t	NOUN
ma-227	61	1	=	=	SYM
ma-227	61	2	ξ	ξ	PROPN
ma-227	61	3	+	+	PUNCT
ma-227	61	4	iη	iη	NOUN
ma-227	61	5	,	,	PUNCT
ma-227	61	6	[	[	X
ma-227	61	7	14	14	NUM
ma-227	61	8	]	]	SYM
ma-227	61	9	.	.	PUNCT
ma-227	62	1	2	2	X
ma-227	62	2	.	.	X
ma-227	62	3	an	an	DET
ma-227	62	4	integral	integral	ADJ
ma-227	62	5	representation	representation	NOUN
ma-227	62	6	formula	formula	NOUN
ma-227	62	7	for	for	ADP
ma-227	62	8	m	m	PRON
ma-227	62	9	in	in	ADP
ma-227	62	10	this	this	DET
ma-227	62	11	section	section	NOUN
ma-227	62	12	,	,	PUNCT
ma-227	62	13	the	the	DET
ma-227	62	14	integral	integral	ADJ
ma-227	62	15	representation	representation	NOUN
ma-227	62	16	formula	formula	NOUN
ma-227	62	17	for	for	ADP
ma-227	62	18	the	the	DET
ma-227	62	19	half	half	ADJ
ma-227	62	20	disc	disc	NOUN
ma-227	62	21	domain	domain	NOUN
ma-227	62	22	is	be	AUX
ma-227	62	23	constructed	construct	VERB
ma-227	62	24	.	.	PUNCT
ma-227	63	1	a	a	DET
ma-227	63	2	con	con	ADJ
ma-227	63	3	-	-	PUNCT
ma-227	63	4	venient	venient	NOUN
ma-227	63	5	technique	technique	NOUN
ma-227	63	6	for	for	ADP
ma-227	63	7	constructing	construct	VERB
ma-227	63	8	the	the	DET
ma-227	63	9	integral	integral	ADJ
ma-227	63	10	representation	representation	NOUN
ma-227	63	11	formula	formula	NOUN
ma-227	63	12	for	for	ADP
ma-227	63	13	domain	domain	NOUN
ma-227	63	14	with	with	ADP
ma-227	63	15	boundariesconsisting	boundariesconsisting	NOUN
ma-227	63	16	of	of	ADP
ma-227	63	17	arcs	arc	NOUN
ma-227	63	18	and	and	CCONJ
ma-227	63	19	straight	straight	ADJ
ma-227	63	20	lines	line	NOUN
ma-227	63	21	is	be	AUX
ma-227	63	22	given	give	VERB
ma-227	63	23	by	by	ADP
ma-227	63	24	the	the	DET
ma-227	63	25	parqueting	parqueting	ADJ
ma-227	63	26	–	–	PUNCT
ma-227	63	27	reflection	reflection	NOUN
ma-227	63	28	method	method	NOUN
ma-227	63	29	.	.	PUNCT
ma-227	64	1	now	now	ADV
ma-227	64	2	using	use	VERB
ma-227	64	3	theparqueting	theparquete	VERB
ma-227	64	4	–	–	PUNCT
ma-227	64	5	reflection	reflection	NOUN
ma-227	64	6	technique	technique	NOUN
ma-227	64	7	for	for	ADP
ma-227	64	8	the	the	DET
ma-227	64	9	introduced	introduce	VERB
ma-227	64	10	domain	domain	NOUN
ma-227	64	11	,	,	PUNCT
ma-227	64	12	we	we	PRON
ma-227	64	13	obtain	obtain	VERB
ma-227	64	14	a	a	DET
ma-227	64	15	cover	cover	NOUN
ma-227	64	16	for	for	ADP
ma-227	64	17	the	the	DET
ma-227	64	18	entire	entire	ADJ
ma-227	64	19	complexplane	complexplane	NOUN
ma-227	64	20	.	.	PUNCT
ma-227	65	1	this	this	DET
ma-227	65	2	coverage	coverage	NOUN
ma-227	65	3	is	be	AUX
ma-227	65	4	obtained	obtain	VERB
ma-227	65	5	from	from	ADP
ma-227	65	6	three	three	NUM
ma-227	65	7	consecutive	consecutive	ADJ
ma-227	65	8	reflections	reflection	NOUN
ma-227	65	9	.	.	PUNCT
ma-227	66	1	reflecting	reflect	VERB
ma-227	66	2	any	any	DET
ma-227	66	3	z	z	NOUN
ma-227	66	4	at	at	ADP
ma-227	66	5	circle	circle	NOUN
ma-227	66	6	gives	give	VERB
ma-227	66	7	|z	|z	PROPN
ma-227	66	8	−	−	PROPN
ma-227	66	9	a|	a|	PROPN
ma-227	67	1	=	=	PUNCT
ma-227	68	1	r	r	NOUN
ma-227	68	2	⇒	⇒	NOUN
ma-227	68	3	(	(	PUNCT
ma-227	68	4	z	z	NOUN
ma-227	68	5	−	−	PROPN
ma-227	68	6	a	a	NOUN
ma-227	68	7	)	)	PUNCT
ma-227	68	8	(	(	PUNCT
ma-227	68	9	z̄	z̄	INTJ
ma-227	68	10	−	−	PRON
ma-227	68	11	a	a	NOUN
ma-227	68	12	)	)	PUNCT
ma-227	68	13	=	=	SYM
ma-227	68	14	r2	r2	PROPN
ma-227	68	15	⇒	⇒	NOUN
ma-227	68	16	zr	zr	PROPN
ma-227	69	1	=	=	PROPN
ma-227	69	2	az̄	az̄	ADV
ma-227	69	3	−	−	PROPN
ma-227	70	1	aa	aa	PROPN
ma-227	70	2	+	+	CCONJ
ma-227	70	3	r2	r2	PROPN
ma-227	70	4	z̄	z̄	PROPN
ma-227	70	5	−	−	PROPN
ma-227	70	6	a	a	PRON
ma-227	70	7	.	.	PUNCT
ma-227	71	1	https://doi.org/10.28924/ada/ma.4.15	https://doi.org/10.28924/ada/ma.4.15	PROPN
ma-227	71	2	eur	eur	PROPN
ma-227	71	3	.	.	PUNCT
ma-227	72	1	j.	j.	PROPN
ma-227	72	2	math	math	PROPN
ma-227	72	3	.	.	PUNCT
ma-227	73	1	anal	anal	PROPN
ma-227	73	2	.	.	PUNCT
ma-227	74	1	10.28924	10.28924	NUM
ma-227	74	2	/	/	SYM
ma-227	74	3	ada	ada	PROPN
ma-227	74	4	/	/	SYM
ma-227	74	5	ma.4.15	ma.4.15	PROPN
ma-227	74	6	4reflecting	4reflecting	NUM
ma-227	74	7	any	any	DET
ma-227	74	8	z	z	NOUN
ma-227	74	9	∈	∈	PROPN
ma-227	74	10	m	m	VERB
ma-227	74	11	at	at	ADP
ma-227	74	12	the	the	DET
ma-227	74	13	d	d	PROPN
ma-227	74	14	,	,	PUNCT
ma-227	74	15	gives	give	VERB
ma-227	74	16	|z	|z	PROPN
ma-227	75	1	|	|	ADV
ma-227	75	2	=	=	SYM
ma-227	75	3	1⇒	1⇒	PROPN
ma-227	75	4	zz̄	zz̄	PROPN
ma-227	75	5	=	=	SYM
ma-227	75	6	1⇒	1⇒	PROPN
ma-227	75	7	z∗	z∗	NOUN
ma-227	75	8	=	=	SYM
ma-227	75	9	1	1	NUM
ma-227	75	10	z̄	z̄	NOUN
ma-227	75	11	.	.	PUNCT
ma-227	76	1	reflecting	reflect	VERB
ma-227	76	2	any	any	DET
ma-227	76	3	z	z	NOUN
ma-227	76	4	at	at	ADP
ma-227	76	5	the	the	DET
ma-227	76	6	real	real	ADJ
ma-227	76	7	axis	axis	NOUN
ma-227	76	8	gives	give	VERB
ma-227	76	9	z̄	z̄	PROPN
ma-227	76	10	.	.	PUNCT
ma-227	77	1	therefore	therefore	ADV
ma-227	77	2	,	,	PUNCT
ma-227	77	3	we	we	PRON
ma-227	77	4	can	can	AUX
ma-227	77	5	obtain	obtain	VERB
ma-227	77	6	the	the	DET
ma-227	77	7	following	follow	VERB
ma-227	77	8	points	point	NOUN
ma-227	77	9	z∗1	z∗1	NOUN
ma-227	77	10	=	=	SYM
ma-227	77	11	1	1	NUM
ma-227	77	12	z̄	z̄	NOUN
ma-227	77	13	,	,	PUNCT
ma-227	77	14	z∗2	z∗2	NOUN
ma-227	77	15	=	=	SYM
ma-227	77	16	1	1	NUM
ma-227	77	17	z	z	NOUN
ma-227	77	18	,	,	PUNCT
ma-227	77	19	z∗3	z∗3	NOUN
ma-227	77	20	=	=	PUNCT
ma-227	77	21	z̄	z̄	PROPN
ma-227	77	22	.	.	PUNCT
ma-227	78	1	those	those	DET
ma-227	78	2	reflections	reflection	NOUN
ma-227	78	3	produce	produce	VERB
ma-227	78	4	a	a	DET
ma-227	78	5	parqueting	parqueting	NOUN
ma-227	78	6	of	of	ADP
ma-227	78	7	the	the	DET
ma-227	78	8	entire	entire	ADJ
ma-227	78	9	complex	complex	ADJ
ma-227	78	10	plane	plane	NOUN
ma-227	78	11	.	.	PUNCT
ma-227	79	1	to	to	PART
ma-227	79	2	solve	solve	VERB
ma-227	79	3	the	the	DET
ma-227	79	4	dirichletboundary	dirichletboundary	ADJ
ma-227	79	5	value	value	NOUN
ma-227	79	6	problems	problem	NOUN
ma-227	79	7	for	for	ADP
ma-227	79	8	analytic	analytic	ADJ
ma-227	79	9	functions	function	NOUN
ma-227	79	10	the	the	DET
ma-227	79	11	integral	integral	ADJ
ma-227	79	12	representation	representation	NOUN
ma-227	79	13	formula	formula	NOUN
ma-227	79	14	is	be	AUX
ma-227	79	15	important.now	important.now	ADJ
ma-227	79	16	,	,	PUNCT
ma-227	79	17	using	use	VERB
ma-227	79	18	the	the	DET
ma-227	79	19	cauchy	cauchy	ADJ
ma-227	79	20	–	–	PUNCT
ma-227	79	21	pompeiu	pompeiu	NOUN
ma-227	79	22	representation	representation	NOUN
ma-227	79	23	formula	formula	NOUN
ma-227	79	24	,	,	PUNCT
ma-227	79	25	we	we	PRON
ma-227	79	26	construct	construct	VERB
ma-227	79	27	the	the	DET
ma-227	79	28	integral	integral	ADJ
ma-227	79	29	representationformula	representationformula	NOUN
ma-227	79	30	for	for	ADP
ma-227	79	31	the	the	DET
ma-227	79	32	half	half	ADJ
ma-227	79	33	disc	disc	NOUN
ma-227	79	34	domain	domain	NOUN
ma-227	79	35	.	.	PUNCT
ma-227	80	1	theorem	theorem	VERB
ma-227	80	2	2.1	2.1	NUM
ma-227	80	3	.	.	PUNCT
ma-227	81	1	any	any	DET
ma-227	81	2	ω	ω	PROPN
ma-227	81	3	∈	∈	PROPN
ma-227	81	4	c1(m;c	c1(m;c	NOUN
ma-227	81	5	)	)	PUNCT
ma-227	81	6	⋂	⋂	PROPN
ma-227	81	7	c(m;c	c(m;c	NOUN
ma-227	81	8	)	)	PUNCT
ma-227	81	9	can	can	AUX
ma-227	81	10	be	be	AUX
ma-227	81	11	represented	represent	VERB
ma-227	81	12	as	as	ADP
ma-227	81	13	ω(z	ω(z	PROPN
ma-227	81	14	)	)	PUNCT
ma-227	81	15	=	=	SYM
ma-227	81	16	1	1	NUM
ma-227	81	17	2πi	2πi	NOUN
ma-227	81	18	∫	∫	PROPN
ma-227	81	19	∂m	∂m	PROPN
ma-227	81	20	ω(t	ω(t	PROPN
ma-227	81	21	)	)	PUNCT
ma-227	81	22	[	[	PUNCT
ma-227	81	23	1	1	NUM
ma-227	81	24	t	t	NOUN
ma-227	81	25	−	−	NOUN
ma-227	81	26	z	z	NOUN
ma-227	82	1	+	+	CCONJ
ma-227	82	2	z	z	NOUN
ma-227	82	3	tz	tz	NOUN
ma-227	82	4	−	−	PROPN
ma-227	82	5	1	1	NUM
ma-227	82	6	]	]	PUNCT
ma-227	82	7	dt	dt	X
ma-227	82	8	−	−	PROPN
ma-227	82	9	1	1	NUM
ma-227	82	10	π	π	PROPN
ma-227	82	11	∫	∫	PROPN
ma-227	82	12	m	m	PROPN
ma-227	82	13	ωt̄(t	ωt̄(t	NUM
ma-227	82	14	)	)	PUNCT
ma-227	82	15	[	[	PUNCT
ma-227	82	16	1	1	NUM
ma-227	82	17	t	t	NOUN
ma-227	82	18	−	−	NOUN
ma-227	82	19	z	z	NOUN
ma-227	83	1	+	+	CCONJ
ma-227	83	2	z	z	NOUN
ma-227	83	3	tz	tz	NOUN
ma-227	83	4	−	−	PROPN
ma-227	83	5	1	1	NUM
ma-227	83	6	]	]	X
ma-227	83	7	dξdη	dξdη	PROPN
ma-227	83	8	,	,	PUNCT
ma-227	83	9	(	(	PUNCT
ma-227	83	10	2.1	2.1	NUM
ma-227	83	11	)	)	PUNCT
ma-227	84	1	where	where	SCONJ
ma-227	84	2	t	t	NOUN
ma-227	84	3	=	=	SYM
ma-227	84	4	ξ	ξ	PROPN
ma-227	85	1	+	+	NUM
ma-227	85	2	iη	iη	NOUN
ma-227	85	3	.	.	PUNCT
ma-227	86	1	proof	proof	NOUN
ma-227	86	2	.	.	PUNCT
ma-227	87	1	applying	apply	VERB
ma-227	87	2	the	the	DET
ma-227	87	3	cauchy	cauchy	NOUN
ma-227	87	4	–	–	PUNCT
ma-227	87	5	pompeiu	pompeiu	NOUN
ma-227	87	6	formula	formula	NOUN
ma-227	87	7	[	[	X
ma-227	87	8	3	3	NUM
ma-227	87	9	]	]	SYM
ma-227	87	10	1	1	NUM
ma-227	87	11	2πi	2πi	NOUN
ma-227	87	12	∫	∫	PROPN
ma-227	87	13	∂m	∂m	PROPN
ma-227	87	14	ω(t	ω(t	PROPN
ma-227	87	15	)	)	PUNCT
ma-227	87	16	dt	dt	PROPN
ma-227	88	1	t	t	NOUN
ma-227	88	2	−	−	PROPN
ma-227	88	3	z	z	NOUN
ma-227	88	4	−	−	NOUN
ma-227	89	1	1	1	NUM
ma-227	89	2	π	π	PROPN
ma-227	89	3	∫	∫	PROPN
ma-227	89	4	m	m	PROPN
ma-227	89	5	ωt̄(t	ωt̄(t	PROPN
ma-227	89	6	)	)	PUNCT
ma-227	89	7	dξdη	dξdη	PROPN
ma-227	89	8	t	t	NOUN
ma-227	89	9	−	−	PROPN
ma-227	89	10	z	z	NOUN
ma-227	89	11	=	=	PRON
ma-227	89	12	{	{	PUNCT
ma-227	89	13	ω(z	ω(z	PROPN
ma-227	89	14	)	)	PUNCT
ma-227	89	15	z	z	NOUN
ma-227	89	16	∈	∈	PROPN
ma-227	89	17	m	m	PROPN
ma-227	89	18	,	,	PUNCT
ma-227	89	19	0	0	NUM
ma-227	89	20	z	z	NOUN
ma-227	89	21	/∈	/∈	PUNCT
ma-227	89	22	m.	m.	NOUN
ma-227	89	23	(	(	PUNCT
ma-227	89	24	2.2	2.2	NUM
ma-227	89	25	)	)	PUNCT
ma-227	89	26	for	for	ADP
ma-227	89	27	z	z	PROPN
ma-227	89	28	∈	∈	PROPN
ma-227	89	29	m	m	NOUN
ma-227	89	30	and	and	CCONJ
ma-227	89	31	z∗2	z∗2	PROPN
ma-227	89	32	/∈	/∈	PROPN
ma-227	90	1	m.	m.	NOUN
ma-227	90	2	substitute	substitute	NOUN
ma-227	90	3	the	the	DET
ma-227	90	4	points	point	NOUN
ma-227	90	5	into	into	ADP
ma-227	90	6	the	the	DET
ma-227	90	7	cauchy	cauchy	NOUN
ma-227	90	8	–	–	PUNCT
ma-227	90	9	pompeiu	pompeiu	NOUN
ma-227	90	10	formula	formula	NOUN
ma-227	90	11	(	(	PUNCT
ma-227	90	12	2.2	2.2	NUM
ma-227	90	13	)	)	PUNCT
ma-227	90	14	ω(z	ω(z	PUNCT
ma-227	90	15	)	)	PUNCT
ma-227	90	16	=	=	SYM
ma-227	90	17	1	1	NUM
ma-227	90	18	2πi	2πi	NOUN
ma-227	90	19	∫	∫	PROPN
ma-227	90	20	∂m	∂m	PROPN
ma-227	90	21	ω(t	ω(t	PROPN
ma-227	90	22	)	)	PUNCT
ma-227	91	1	dt	dt	PROPN
ma-227	91	2	t	t	NOUN
ma-227	92	1	−	−	PROPN
ma-227	92	2	z	z	NOUN
ma-227	93	1	−	−	NOUN
ma-227	93	2	1	1	NUM
ma-227	93	3	π	π	PROPN
ma-227	93	4	∫	∫	PROPN
ma-227	93	5	m	m	PROPN
ma-227	93	6	ωt̄(t	ωt̄(t	PROPN
ma-227	93	7	)	)	PUNCT
ma-227	93	8	dξdη	dξdη	PROPN
ma-227	93	9	t	t	PROPN
ma-227	93	10	−	−	PROPN
ma-227	93	11	z	z	NOUN
ma-227	93	12	.	.	PUNCT
ma-227	94	1	(	(	PUNCT
ma-227	94	2	2.3	2.3	NUM
ma-227	94	3	)	)	PUNCT
ma-227	94	4	since	since	SCONJ
ma-227	94	5	point	point	NOUN
ma-227	94	6	z∗2	z∗2	NOUN
ma-227	94	7	is	be	AUX
ma-227	94	8	outside	outside	ADP
ma-227	94	9	the	the	DET
ma-227	94	10	domain	domain	NOUN
ma-227	94	11	m	m	VERB
ma-227	94	12	,	,	PUNCT
ma-227	94	13	therefore	therefore	ADV
ma-227	94	14	,	,	PUNCT
ma-227	94	15	the	the	DET
ma-227	94	16	cauchy	cauchy	PROPN
ma-227	94	17	–	–	PUNCT
ma-227	94	18	pompeiu	pompeiu	NOUN
ma-227	94	19	formula	formula	NOUN
ma-227	94	20	is	be	AUX
ma-227	94	21	equal	equal	ADJ
ma-227	94	22	to	to	ADP
ma-227	94	23	zeroat	zeroat	NOUN
ma-227	94	24	this	this	DET
ma-227	94	25	point	point	NOUN
ma-227	94	26	.	.	PUNCT
ma-227	94	27	0	0	PUNCT
ma-227	95	1	=	=	SYM
ma-227	95	2	1	1	NUM
ma-227	95	3	2πi	2πi	NOUN
ma-227	95	4	∫	∫	PROPN
ma-227	95	5	∂m	∂m	PROPN
ma-227	95	6	ω(t	ω(t	PROPN
ma-227	95	7	)	)	PUNCT
ma-227	95	8	zdt	zdt	PROPN
ma-227	96	1	tz	tz	PROPN
ma-227	96	2	−	−	NUM
ma-227	96	3	1	1	NUM
ma-227	96	4	−	−	NOUN
ma-227	96	5	1	1	NUM
ma-227	96	6	π	π	PROPN
ma-227	96	7	∫	∫	PROPN
ma-227	96	8	m	m	PROPN
ma-227	96	9	ωt̄(t	ωt̄(t	PROPN
ma-227	96	10	)	)	PUNCT
ma-227	96	11	zdξdη	zdξdη	PROPN
ma-227	97	1	tz	tz	NOUN
ma-227	97	2	−	−	NUM
ma-227	97	3	1	1	NUM
ma-227	97	4	,	,	PUNCT
ma-227	97	5	(	(	PUNCT
ma-227	97	6	2.4	2.4	NUM
ma-227	97	7	)	)	PUNCT
ma-227	97	8	by	by	ADP
ma-227	97	9	combining	combine	VERB
ma-227	97	10	the	the	DET
ma-227	97	11	obtained	obtain	VERB
ma-227	97	12	equations	equation	NOUN
ma-227	97	13	,	,	PUNCT
ma-227	97	14	the	the	DET
ma-227	97	15	integral	integral	ADJ
ma-227	97	16	representation	representation	NOUN
ma-227	97	17	formula	formula	NOUN
ma-227	97	18	is	be	AUX
ma-227	97	19	obtained	obtain	VERB
ma-227	97	20	.	.	PUNCT
ma-227	98	1	�	�	PROPN
ma-227	98	2	the	the	DET
ma-227	98	3	integral	integral	ADJ
ma-227	98	4	representation	representation	NOUN
ma-227	98	5	formula	formula	NOUN
ma-227	98	6	(	(	PUNCT
ma-227	98	7	2.1	2.1	NUM
ma-227	98	8	)	)	PUNCT
ma-227	98	9	,	,	PUNCT
ma-227	98	10	serves	serve	VERB
ma-227	98	11	to	to	PART
ma-227	98	12	solve	solve	VERB
ma-227	98	13	the	the	DET
ma-227	98	14	related	related	ADJ
ma-227	98	15	the	the	DET
ma-227	98	16	dirichlet	dirichlet	PROPN
ma-227	98	17	problem	problem	NOUN
ma-227	98	18	forthe	forthe	PROPN
ma-227	98	19	cauchy	cauchy	PROPN
ma-227	98	20	–	–	PUNCT
ma-227	98	21	riemann	riemann	PROPN
ma-227	98	22	equations	equation	NOUN
ma-227	98	23	in	in	ADP
ma-227	98	24	m	m	PROPN
ma-227	98	25	.	.	PUNCT
ma-227	99	1	3	3	X
ma-227	99	2	.	.	X
ma-227	99	3	dirichlet	dirichlet	PROPN
ma-227	99	4	problem	problem	NOUN
ma-227	99	5	for	for	ADP
ma-227	99	6	the	the	DET
ma-227	99	7	cauchy	cauchy	PROPN
ma-227	99	8	–	–	PUNCT
ma-227	99	9	riemann	riemann	PROPN
ma-227	99	10	equation	equation	NOUN
ma-227	99	11	in	in	ADP
ma-227	99	12	m	m	PROPN
ma-227	99	13	in	in	ADP
ma-227	99	14	this	this	DET
ma-227	99	15	section	section	NOUN
ma-227	99	16	,	,	PUNCT
ma-227	99	17	we	we	PRON
ma-227	99	18	study	study	VERB
ma-227	99	19	the	the	DET
ma-227	99	20	dirichlet	dirichlet	PROPN
ma-227	99	21	boundary	boundary	PROPN
ma-227	99	22	value	value	NOUN
ma-227	99	23	problem	problem	NOUN
ma-227	99	24	for	for	ADP
ma-227	99	25	the	the	DET
ma-227	99	26	homogeneous	homogeneous	ADJ
ma-227	99	27	and	and	CCONJ
ma-227	99	28	the	the	DET
ma-227	99	29	in	in	ADP
ma-227	99	30	-	-	PUNCT
ma-227	99	31	homogeneous	homogeneous	ADJ
ma-227	99	32	cauchy	cauchy	PROPN
ma-227	99	33	–	–	PUNCT
ma-227	99	34	riemann	riemann	PROPN
ma-227	99	35	equations	equation	NOUN
ma-227	99	36	.	.	PUNCT
ma-227	100	1	in	in	ADP
ma-227	100	2	the	the	DET
ma-227	100	3	following	following	NOUN
ma-227	100	4	,	,	PUNCT
ma-227	100	5	we	we	PRON
ma-227	100	6	solve	solve	VERB
ma-227	100	7	the	the	DET
ma-227	100	8	dirichlet	dirichlet	PROPN
ma-227	100	9	boundary	boundary	ADJ
ma-227	100	10	valueproblem	valueproblem	NOUN
ma-227	100	11	for	for	ADP
ma-227	100	12	the	the	DET
ma-227	100	13	homogeneous	homogeneous	ADJ
ma-227	100	14	cauchy	cauchy	PROPN
ma-227	100	15	–	–	PUNCT
ma-227	100	16	riemann	riemann	PROPN
ma-227	100	17	equation	equation	NOUN
ma-227	100	18	.	.	PUNCT
ma-227	101	1	https://doi.org/10.28924/ada/ma.4.15	https://doi.org/10.28924/ada/ma.4.15	PROPN
ma-227	101	2	eur	eur	PROPN
ma-227	101	3	.	.	PUNCT
ma-227	102	1	j.	j.	PROPN
ma-227	102	2	math	math	PROPN
ma-227	102	3	.	.	PUNCT
ma-227	103	1	anal	anal	PROPN
ma-227	103	2	.	.	PUNCT
ma-227	104	1	10.28924	10.28924	NUM
ma-227	104	2	/	/	SYM
ma-227	104	3	ada	ada	PROPN
ma-227	104	4	/	/	SYM
ma-227	104	5	ma.4.15	ma.4.15	PROPN
ma-227	104	6	5	5	NUM
ma-227	104	7	theorem	theorem	VERB
ma-227	104	8	3.1	3.1	NUM
ma-227	104	9	.	.	PUNCT
ma-227	105	1	the	the	DET
ma-227	105	2	dirichlet	dirichlet	PROPN
ma-227	105	3	problem	problem	NOUN
ma-227	105	4	for	for	ADP
ma-227	105	5	the	the	DET
ma-227	105	6	homogeneous	homogeneous	ADJ
ma-227	105	7	cauchy	cauchy	PROPN
ma-227	105	8	–	–	PUNCT
ma-227	105	9	riemann	riemann	PROPN
ma-227	105	10	equation	equation	PUNCT
ma-227	105	11	ωz̄	ωz̄	NOUN
ma-227	105	12	=	=	SYM
ma-227	105	13	0	0	NUM
ma-227	105	14	,	,	PUNCT
ma-227	105	15	in	in	ADP
ma-227	105	16	m	m	PROPN
ma-227	105	17	,	,	PUNCT
ma-227	105	18	ω	ω	PROPN
ma-227	105	19	=	=	SYM
ma-227	105	20	γ	γ	PROPN
ma-227	105	21	,	,	PUNCT
ma-227	105	22	on	on	ADP
ma-227	105	23	∂m	∂m	PROPN
ma-227	105	24	,	,	PUNCT
ma-227	105	25	γ	γ	PROPN
ma-227	105	26	∈	∈	PROPN
ma-227	105	27	c(∂m;c	c(∂m;c	PROPN
ma-227	105	28	)	)	PUNCT
ma-227	105	29	(	(	PUNCT
ma-227	105	30	3.1	3.1	NUM
ma-227	105	31	)	)	PUNCT
ma-227	105	32	with	with	ADP
ma-227	105	33	given	give	VERB
ma-227	105	34	γ	γ	PROPN
ma-227	105	35	∈	∈	PROPN
ma-227	105	36	c(∂m;c	c(∂m;c	NOUN
ma-227	105	37	)	)	PUNCT
ma-227	105	38	,	,	PUNCT
ma-227	105	39	γ(±1	γ(±1	PROPN
ma-227	105	40	)	)	PUNCT
ma-227	105	41	=	=	SYM
ma-227	105	42	0	0	NUM
ma-227	105	43	,	,	PUNCT
ma-227	105	44	is	be	AUX
ma-227	105	45	solvable	solvable	ADJ
ma-227	105	46	,	,	PUNCT
ma-227	105	47	if	if	SCONJ
ma-227	105	48	and	and	CCONJ
ma-227	105	49	only	only	ADV
ma-227	105	50	if	if	SCONJ
ma-227	105	51	1	1	NUM
ma-227	105	52	2πi	2πi	NOUN
ma-227	105	53	∫	∫	PROPN
ma-227	105	54	∂m	∂m	X
ma-227	105	55	γ(t	γ(t	PROPN
ma-227	105	56	)	)	PUNCT
ma-227	106	1	[	[	PUNCT
ma-227	106	2	1	1	NUM
ma-227	106	3	t	t	NOUN
ma-227	106	4	−	−	PROPN
ma-227	106	5	z̄	z̄	PROPN
ma-227	106	6	+	+	CCONJ
ma-227	106	7	z̄	z̄	CCONJ
ma-227	106	8	tz̄	tz̄	NOUN
ma-227	106	9	−	−	NOUN
ma-227	106	10	1	1	NUM
ma-227	106	11	]	]	PUNCT
ma-227	106	12	dt	dt	X
ma-227	106	13	=	=	SYM
ma-227	106	14	0	0	NUM
ma-227	106	15	,	,	PUNCT
ma-227	106	16	(	(	PUNCT
ma-227	106	17	3.2	3.2	NUM
ma-227	106	18	)	)	PUNCT
ma-227	106	19	and	and	CCONJ
ma-227	106	20	the	the	DET
ma-227	106	21	unique	unique	ADJ
ma-227	106	22	solution	solution	NOUN
ma-227	106	23	can	can	AUX
ma-227	106	24	be	be	AUX
ma-227	106	25	presented	present	VERB
ma-227	106	26	as	as	ADP
ma-227	106	27	ω(z	ω(z	PROPN
ma-227	106	28	)	)	PUNCT
ma-227	106	29	=	=	SYM
ma-227	106	30	1	1	NUM
ma-227	106	31	2πi	2πi	NOUN
ma-227	106	32	∫	∫	PROPN
ma-227	106	33	∂m	∂m	PROPN
ma-227	106	34	γ(t	γ(t	PROPN
ma-227	106	35	)	)	PUNCT
ma-227	106	36	[	[	PUNCT
ma-227	106	37	1	1	NUM
ma-227	106	38	t	t	NOUN
ma-227	106	39	−	−	NOUN
ma-227	106	40	z	z	NOUN
ma-227	107	1	+	+	CCONJ
ma-227	107	2	z	z	NOUN
ma-227	107	3	tz	tz	NOUN
ma-227	107	4	−	−	PROPN
ma-227	107	5	1	1	NUM
ma-227	107	6	]	]	PUNCT
ma-227	107	7	dt	dt	X
ma-227	107	8	,	,	PUNCT
ma-227	107	9	z	z	PROPN
ma-227	107	10	∈	∈	PROPN
ma-227	107	11	m.	m.	NOUN
ma-227	107	12	(	(	PUNCT
ma-227	107	13	3.3	3.3	NUM
ma-227	107	14	)	)	PUNCT
ma-227	107	15	proof	proof	NOUN
ma-227	107	16	.	.	PUNCT
ma-227	108	1	let	let	VERB
ma-227	108	2	ω	ω	NUM
ma-227	108	3	defined	define	VERB
ma-227	108	4	by	by	ADP
ma-227	108	5	(	(	PUNCT
ma-227	108	6	3.3	3.3	NUM
ma-227	108	7	)	)	PUNCT
ma-227	108	8	be	be	AUX
ma-227	108	9	a	a	DET
ma-227	108	10	solution	solution	NOUN
ma-227	108	11	to	to	ADP
ma-227	108	12	the	the	DET
ma-227	108	13	dirichlet	dirichlet	PROPN
ma-227	108	14	problem	problem	NOUN
ma-227	108	15	.	.	PUNCT
ma-227	109	1	then	then	ADV
ma-227	109	2	the	the	DET
ma-227	109	3	equality	equality	NOUN
ma-227	109	4	ω(z	ω(z	PUNCT
ma-227	109	5	)	)	PUNCT
ma-227	109	6	=	=	PUNCT
ma-227	109	7	γ(t	γ(t	NOUN
ma-227	109	8	)	)	PUNCT
ma-227	109	9	,	,	PUNCT
ma-227	109	10	t	t	PROPN
ma-227	109	11	∈	∈	PROPN
ma-227	109	12	∂m	∂m	PROPN
ma-227	109	13	,	,	PUNCT
ma-227	109	14	(	(	PUNCT
ma-227	109	15	3.4	3.4	NUM
ma-227	109	16	)	)	PUNCT
ma-227	109	17	holds	hold	VERB
ma-227	109	18	.	.	PUNCT
ma-227	110	1	we	we	PRON
ma-227	110	2	consider	consider	VERB
ma-227	110	3	the	the	DET
ma-227	110	4	following	follow	VERB
ma-227	110	5	function	function	NOUN
ma-227	110	6	h(z	h(z	NOUN
ma-227	110	7	)	)	PUNCT
ma-227	110	8	=	=	SYM
ma-227	110	9	1	1	NUM
ma-227	110	10	2πi	2πi	NOUN
ma-227	110	11	∫	∫	PROPN
ma-227	110	12	∂m	∂m	PROPN
ma-227	110	13	γ(t	γ(t	PROPN
ma-227	110	14	)	)	PUNCT
ma-227	111	1	[	[	PUNCT
ma-227	111	2	1	1	NUM
ma-227	111	3	t	t	NOUN
ma-227	111	4	−	−	PROPN
ma-227	111	5	z̄	z̄	PROPN
ma-227	111	6	+	+	CCONJ
ma-227	111	7	z̄	z̄	CCONJ
ma-227	111	8	tz̄	tz̄	NOUN
ma-227	111	9	−	−	NOUN
ma-227	111	10	1	1	NUM
ma-227	111	11	]	]	PUNCT
ma-227	111	12	dt	dt	X
ma-227	111	13	,	,	PUNCT
ma-227	111	14	(	(	PUNCT
ma-227	111	15	3.5	3.5	NUM
ma-227	111	16	)	)	PUNCT
ma-227	111	17	and	and	CCONJ
ma-227	111	18	take	take	VERB
ma-227	111	19	the	the	DET
ma-227	111	20	difference	difference	NOUN
ma-227	111	21	ω(z)−	ω(z)−	NOUN
ma-227	111	22	h(z	h(z	NOUN
ma-227	111	23	)	)	PUNCT
ma-227	111	24	=	=	SYM
ma-227	111	25	1	1	NUM
ma-227	111	26	2πi	2πi	NOUN
ma-227	111	27	∫	∫	PROPN
ma-227	111	28	∂m	∂m	PROPN
ma-227	111	29	γ(t	γ(t	PROPN
ma-227	111	30	)	)	PUNCT
ma-227	111	31	[	[	PUNCT
ma-227	111	32	1	1	NUM
ma-227	111	33	ζ	ζ	NOUN
ma-227	111	34	−	−	PROPN
ma-227	111	35	z	z	NOUN
ma-227	112	1	+	+	NOUN
ma-227	112	2	z	z	NOUN
ma-227	112	3	tz	tz	NOUN
ma-227	112	4	−	−	PROPN
ma-227	112	5	1	1	NUM
ma-227	112	6	]	]	PUNCT
ma-227	112	7	dt	dt	X
ma-227	112	8	−	−	PROPN
ma-227	112	9	1	1	NUM
ma-227	112	10	2πi	2πi	NOUN
ma-227	112	11	∫	∫	PROPN
ma-227	112	12	∂m	∂m	PROPN
ma-227	112	13	γ(t	γ(t	PROPN
ma-227	112	14	)	)	PUNCT
ma-227	112	15	[	[	PUNCT
ma-227	112	16	1	1	NUM
ma-227	112	17	t	t	NOUN
ma-227	112	18	−	−	PROPN
ma-227	112	19	z̄	z̄	PROPN
ma-227	112	20	+	+	CCONJ
ma-227	112	21	z̄	z̄	CCONJ
ma-227	112	22	tz̄	tz̄	NOUN
ma-227	112	23	−	−	NOUN
ma-227	112	24	1	1	NUM
ma-227	112	25	]	]	PUNCT
ma-227	112	26	dt	dt	X
ma-227	112	27	=	=	SYM
ma-227	112	28	1	1	NUM
ma-227	112	29	2πi	2πi	NOUN
ma-227	112	30	∫	∫	PROPN
ma-227	112	31	∂m	∂m	PROPN
ma-227	112	32	γ(t	γ(t	PROPN
ma-227	112	33	)	)	PUNCT
ma-227	112	34	[	[	PUNCT
ma-227	112	35	1	1	NUM
ma-227	112	36	t	t	NOUN
ma-227	112	37	−	−	PROPN
ma-227	112	38	z	z	NOUN
ma-227	113	1	−	−	PROPN
ma-227	113	2	1	1	NUM
ma-227	113	3	t	t	NOUN
ma-227	113	4	−	−	PROPN
ma-227	113	5	z̄	z̄	PROPN
ma-227	114	1	+	+	CCONJ
ma-227	114	2	z	z	NOUN
ma-227	114	3	tz	tz	NOUN
ma-227	114	4	−	−	NUM
ma-227	114	5	1	1	NUM
ma-227	114	6	−	−	PROPN
ma-227	114	7	z̄	z̄	NOUN
ma-227	114	8	tz̄	tz̄	NOUN
ma-227	114	9	−	−	NOUN
ma-227	114	10	1	1	NUM
ma-227	114	11	]	]	PUNCT
ma-227	114	12	dt	dt	X
ma-227	114	13	=	=	SYM
ma-227	114	14	1	1	NUM
ma-227	114	15	2πi	2πi	ADJ
ma-227	114	16	∫	∫	PROPN
ma-227	114	17	∂m∩d	∂m∩d	NUM
ma-227	114	18	γ(t	γ(t	NOUN
ma-227	114	19	)	)	PUNCT
ma-227	115	1	[	[	PUNCT
ma-227	115	2	t	t	PROPN
ma-227	115	3	t	t	X
ma-227	115	4	−	−	PROPN
ma-227	115	5	z	z	PROPN
ma-227	116	1	+	+	NUM
ma-227	116	2	t̄	t̄	PROPN
ma-227	116	3	t̄	t̄	PROPN
ma-227	116	4	−	−	PROPN
ma-227	116	5	z̄	z̄	PROPN
ma-227	116	6	−	−	PROPN
ma-227	116	7	t̄	t̄	PROPN
ma-227	116	8	t̄	t̄	PROPN
ma-227	117	1	−	−	PROPN
ma-227	117	2	z	z	NOUN
ma-227	118	1	−	−	PROPN
ma-227	118	2	t	t	PROPN
ma-227	118	3	t	t	PROPN
ma-227	118	4	−	−	PROPN
ma-227	118	5	z̄	z̄	PROPN
ma-227	118	6	]	]	PUNCT
ma-227	118	7	dt	dt	X
ma-227	119	1	t	t	PROPN
ma-227	119	2	+	+	CCONJ
ma-227	119	3	1	1	NUM
ma-227	119	4	2πi	2πi	ADJ
ma-227	119	5	∫	∫	NOUN
ma-227	119	6	1	1	NUM
ma-227	119	7	−1	−1	NOUN
ma-227	119	8	γ(s	γ(	NOUN
ma-227	119	9	)	)	PUNCT
ma-227	119	10	[	[	PUNCT
ma-227	119	11	1	1	NUM
ma-227	119	12	s	s	NOUN
ma-227	119	13	−	−	PROPN
ma-227	119	14	z	z	NOUN
ma-227	119	15	−	−	PROPN
ma-227	119	16	1	1	NUM
ma-227	119	17	s	s	NOUN
ma-227	119	18	−	−	PROPN
ma-227	119	19	z̄	z̄	PROPN
ma-227	119	20	+	+	CCONJ
ma-227	119	21	z	z	PROPN
ma-227	119	22	sz	sz	NOUN
ma-227	119	23	−	−	NUM
ma-227	119	24	1	1	NUM
ma-227	119	25	−	−	PROPN
ma-227	119	26	z̄	z̄	X
ma-227	119	27	s	s	PART
ma-227	119	28	z̄	z̄	X
ma-227	119	29	−	−	ADP
ma-227	119	30	1	1	NUM
ma-227	119	31	]	]	PUNCT
ma-227	119	32	ds	ds	NOUN
ma-227	119	33	=	=	SYM
ma-227	119	34	1	1	NUM
ma-227	119	35	2πi	2πi	ADJ
ma-227	119	36	∫	∫	PROPN
ma-227	120	1	∂m∩d	∂m∩d	NUM
ma-227	120	2	γ(t	γ(t	NOUN
ma-227	120	3	)	)	PUNCT
ma-227	120	4	[	[	PUNCT
ma-227	120	5	1−	1−	NUM
ma-227	120	6	|z	|z	PROPN
ma-227	120	7	|2	|2	NUM
ma-227	120	8	|t	|t	PROPN
ma-227	120	9	−	−	PROPN
ma-227	120	10	z	z	NOUN
ma-227	120	11	|2	|2	NUM
ma-227	121	1	−	−	PROPN
ma-227	121	2	1−	1−	NUM
ma-227	121	3	|z	|z	PROPN
ma-227	121	4	|2	|2	NUM
ma-227	121	5	|t̄	|t̄	PROPN
ma-227	121	6	−	−	PROPN
ma-227	121	7	z	z	PROPN
ma-227	121	8	|2	|2	NUM
ma-227	121	9	]	]	PUNCT
ma-227	121	10	dt	dt	X
ma-227	121	11	t	t	PROPN
ma-227	121	12	+	+	CCONJ
ma-227	121	13	1	1	NUM
ma-227	121	14	2πi	2πi	ADJ
ma-227	121	15	∫	∫	NOUN
ma-227	121	16	1	1	NUM
ma-227	121	17	−1	−1	NOUN
ma-227	121	18	γ(s	γ(	NOUN
ma-227	121	19	)	)	PUNCT
ma-227	122	1	[	[	PUNCT
ma-227	122	2	z	z	NOUN
ma-227	122	3	−	−	PROPN
ma-227	122	4	z̄	z̄	X
ma-227	122	5	|s	|s	PROPN
ma-227	122	6	−	−	PROPN
ma-227	122	7	z	z	NOUN
ma-227	122	8	|2	|2	NUM
ma-227	123	1	−	−	PROPN
ma-227	123	2	z	z	NOUN
ma-227	123	3	−	−	PROPN
ma-227	123	4	z̄	z̄	INTJ
ma-227	123	5	|1−	|1−	INTJ
ma-227	123	6	zs|2	zs|2	NOUN
ma-227	123	7	]	]	X
ma-227	123	8	ds	ds	X
ma-227	123	9	.	.	PUNCT
ma-227	124	1	studying	study	VERB
ma-227	124	2	the	the	DET
ma-227	124	3	boundary	boundary	ADJ
ma-227	124	4	behavior	behavior	NOUN
ma-227	124	5	of	of	ADP
ma-227	124	6	the	the	DET
ma-227	124	7	boundary	boundary	ADJ
ma-227	124	8	integral	integral	ADJ
ma-227	124	9	implies	imply	VERB
ma-227	124	10	computations	computation	NOUN
ma-227	124	11	on	on	ADP
ma-227	124	12	the	the	DET
ma-227	124	13	differentparts	differentpart	NOUN
ma-227	124	14	of	of	ADP
ma-227	124	15	the	the	DET
ma-227	124	16	boundary	boundary	NOUN
ma-227	124	17	∂m	∂m	PROPN
ma-227	124	18	.	.	PUNCT
ma-227	125	1	for	for	ADP
ma-227	125	2	|t0|	|t0|	NOUN
ma-227	125	3	=	=	SYM
ma-227	125	4	1	1	NUM
ma-227	125	5	,	,	PUNCT
ma-227	125	6	imt0	imt0	VERB
ma-227	125	7	>	>	X
ma-227	125	8	0	0	X
ma-227	125	9	.	.	PUNCT
ma-227	126	1	as	as	ADP
ma-227	126	2	|t̄	|t̄	PROPN
ma-227	126	3	−	−	PROPN
ma-227	126	4	t0|2	t0|2	PROPN
ma-227	126	5	6=	6=	ADP
ma-227	126	6	0	0	NUM
ma-227	126	7	,	,	PUNCT
ma-227	126	8	1−	1−	NUM
ma-227	126	9	|t0|2	|t0|2	NUM
ma-227	126	10	=	=	SYM
ma-227	126	11	0	0	NUM
ma-227	126	12	and	and	CCONJ
ma-227	126	13	|s	|s	PROPN
ma-227	126	14	−	−	PROPN
ma-227	126	15	t0|2	t0|2	NOUN
ma-227	126	16	=	=	SYM
ma-227	126	17	|1−	|1−	INTJ
ma-227	126	18	t0s|2	t0s|2	PROPN
ma-227	126	19	.	.	PUNCT
ma-227	127	1	thus	thus	ADV
ma-227	127	2	,	,	PUNCT
ma-227	127	3	lim	lim	PROPN
ma-227	127	4	z→t	z→t	NUM
ma-227	127	5	(	(	PUNCT
ma-227	127	6	ω(z)−	ω(z)−	PROPN
ma-227	127	7	h(z	h(z	NOUN
ma-227	127	8	)	)	PUNCT
ma-227	127	9	)	)	PUNCT
ma-227	127	10	=	=	PUNCT
ma-227	127	11	γ(t).for	γ(t).for	ADP
ma-227	127	12	|t0|	|t0|	NOUN
ma-227	127	13	<	<	X
ma-227	127	14	1	1	NUM
ma-227	127	15	,	,	PUNCT
ma-227	127	16	imt0	imt0	NOUN
ma-227	127	17	=	=	SYM
ma-227	127	18	0	0	X
ma-227	127	19	.	.	PUNCT
ma-227	128	1	since	since	SCONJ
ma-227	128	2	|t	|t	PROPN
ma-227	128	3	−	−	NOUN
ma-227	128	4	t0|	t0|	X
ma-227	128	5	=	=	SYM
ma-227	128	6	|t̄	|t̄	PROPN
ma-227	128	7	−	−	PROPN
ma-227	128	8	t0|	t0|	X
ma-227	128	9	,	,	PUNCT
ma-227	128	10	|1−	|1−	VERB
ma-227	128	11	t0s|2	t0s|2	PROPN
ma-227	128	12	6=	6=	ADP
ma-227	128	13	0	0	NUM
ma-227	128	14	,	,	PUNCT
ma-227	128	15	t	t	NOUN
ma-227	128	16	−	−	NOUN
ma-227	128	17	t̄0	t̄0	NOUN
ma-227	128	18	=	=	SYM
ma-227	128	19	0	0	NUM
ma-227	128	20	.	.	PUNCT
ma-227	129	1	thus	thus	ADV
ma-227	129	2	,	,	PUNCT
ma-227	129	3	lim	lim	PROPN
ma-227	129	4	z→t	z→t	NUM
ma-227	129	5	(	(	PUNCT
ma-227	129	6	ω(z)−	ω(z)−	PROPN
ma-227	129	7	h(z	h(z	NOUN
ma-227	129	8	)	)	PUNCT
ma-227	129	9	)	)	PUNCT
ma-227	130	1	=	=	PUNCT
ma-227	130	2	γ(t	γ(t	NOUN
ma-227	130	3	)	)	PUNCT
ma-227	130	4	.	.	PUNCT
ma-227	131	1	now	now	ADV
ma-227	131	2	,	,	PUNCT
ma-227	131	3	we	we	PRON
ma-227	131	4	consider	consider	VERB
ma-227	131	5	the	the	DET
ma-227	131	6	boundary	boundary	ADJ
ma-227	131	7	behavior	behavior	NOUN
ma-227	131	8	at	at	ADP
ma-227	131	9	the	the	DET
ma-227	131	10	corner	corner	NOUN
ma-227	131	11	points	point	NOUN
ma-227	131	12	.	.	PUNCT
ma-227	132	1	let	let	VERB
ma-227	132	2	ω(z)−	ω(z)−	PROPN
ma-227	132	3	h(z	h(z	NOUN
ma-227	132	4	)	)	PUNCT
ma-227	132	5	=	=	SYM
ma-227	132	6	1	1	NUM
ma-227	132	7	2πi	2πi	ADJ
ma-227	132	8	∫	∫	PROPN
ma-227	132	9	∂m∩d	∂m∩d	NUM
ma-227	132	10	γ(t	γ(t	NOUN
ma-227	132	11	)	)	PUNCT
ma-227	133	1	[	[	PUNCT
ma-227	133	2	t	t	NOUN
ma-227	133	3	+	+	CCONJ
ma-227	133	4	z	z	PROPN
ma-227	133	5	t	t	NOUN
ma-227	133	6	−	−	PROPN
ma-227	133	7	z	z	NOUN
ma-227	133	8	−	−	PROPN
ma-227	133	9	t̄	t̄	NOUN
ma-227	134	1	+	+	CCONJ
ma-227	134	2	z	z	PROPN
ma-227	134	3	t̄	t̄	NOUN
ma-227	134	4	−	−	PROPN
ma-227	135	1	z	z	PROPN
ma-227	135	2	]	]	PUNCT
ma-227	135	3	dt	dt	X
ma-227	136	1	t	t	PROPN
ma-227	136	2	https://doi.org/10.28924/ada/ma.4.15	https://doi.org/10.28924/ada/ma.4.15	PROPN
ma-227	136	3	eur	eur	PROPN
ma-227	136	4	.	.	PUNCT
ma-227	137	1	j.	j.	PROPN
ma-227	137	2	math	math	PROPN
ma-227	137	3	.	.	PUNCT
ma-227	138	1	anal	anal	PROPN
ma-227	138	2	.	.	PUNCT
ma-227	139	1	10.28924	10.28924	NUM
ma-227	139	2	/	/	SYM
ma-227	139	3	ada	ada	PROPN
ma-227	139	4	/	/	SYM
ma-227	139	5	ma.4.15	ma.4.15	PROPN
ma-227	139	6	6we	6we	NOUN
ma-227	139	7	can	can	AUX
ma-227	139	8	write	write	VERB
ma-227	139	9	ω(z)−	ω(z)−	PROPN
ma-227	139	10	h(z	h(z	NOUN
ma-227	139	11	)	)	PUNCT
ma-227	139	12	=	=	SYM
ma-227	139	13	1	1	NUM
ma-227	139	14	2πi	2πi	ADJ
ma-227	139	15	∫	∫	PROPN
ma-227	139	16	∂m∩d	∂m∩d	NUM
ma-227	139	17	γ(t	γ(t	NOUN
ma-227	139	18	)	)	PUNCT
ma-227	139	19	t	t	NOUN
ma-227	140	1	+	+	CCONJ
ma-227	140	2	z	z	PROPN
ma-227	140	3	t	t	NOUN
ma-227	140	4	−	−	PROPN
ma-227	141	1	z	z	NOUN
ma-227	141	2	dt	dt	NOUN
ma-227	142	1	t	t	NOUN
ma-227	143	1	+	+	CCONJ
ma-227	143	2	1	1	NUM
ma-227	143	3	2πi	2πi	ADJ
ma-227	143	4	∫	∫	NOUN
ma-227	144	1	∂m∩d	∂m∩d	NUM
ma-227	144	2	γ(t	γ(t	NOUN
ma-227	144	3	)	)	PUNCT
ma-227	144	4	t̄	t̄	NOUN
ma-227	145	1	+	+	CCONJ
ma-227	145	2	z	z	PROPN
ma-227	145	3	t̄	t̄	NOUN
ma-227	145	4	−	−	PROPN
ma-227	146	1	z	z	NOUN
ma-227	146	2	dt	dt	PROPN
ma-227	146	3	t̄	t̄	NOUN
ma-227	147	1	=	=	SYM
ma-227	147	2	1	1	NUM
ma-227	147	3	2πi	2πi	ADJ
ma-227	147	4	∫	∫	PROPN
ma-227	147	5	∂m∩d	∂m∩d	NUM
ma-227	147	6	γ(t	γ(t	NOUN
ma-227	147	7	)	)	PUNCT
ma-227	148	1	t	t	NOUN
ma-227	149	1	+	+	CCONJ
ma-227	149	2	z	z	PROPN
ma-227	149	3	t	t	NOUN
ma-227	149	4	−	−	PROPN
ma-227	150	1	z	z	NOUN
ma-227	150	2	dt	dt	NOUN
ma-227	150	3	t	t	NOUN
ma-227	150	4	−	−	NUM
ma-227	150	5	1	1	NUM
ma-227	150	6	2πi	2πi	ADJ
ma-227	150	7	∫	∫	PROPN
ma-227	150	8	∂m∩d	∂m∩d	NUM
ma-227	150	9	γ(t̄	γ(t̄	NOUN
ma-227	150	10	)	)	PUNCT
ma-227	150	11	t	t	NOUN
ma-227	151	1	+	+	CCONJ
ma-227	151	2	z	z	PROPN
ma-227	151	3	t	t	NOUN
ma-227	151	4	−	−	PROPN
ma-227	152	1	z	z	NOUN
ma-227	152	2	dt	dt	NOUN
ma-227	152	3	t	t	NOUN
ma-227	152	4	=	=	SYM
ma-227	152	5	1	1	NUM
ma-227	152	6	2πi	2πi	ADJ
ma-227	152	7	∫	∫	PROPN
ma-227	152	8	∂m∩d	∂m∩d	NUM
ma-227	152	9	υ(t	υ(t	NOUN
ma-227	152	10	)	)	PUNCT
ma-227	152	11	t	t	NOUN
ma-227	153	1	+	+	CCONJ
ma-227	153	2	z	z	PROPN
ma-227	153	3	t	t	NOUN
ma-227	153	4	−	−	PROPN
ma-227	154	1	z	z	NOUN
ma-227	154	2	dt	dt	NOUN
ma-227	154	3	twhere	twhere	ADP
ma-227	154	4	υ(t	υ(t	NOUN
ma-227	154	5	)	)	PUNCT
ma-227	155	1	=	=	PRON
ma-227	155	2	{	{	PUNCT
ma-227	155	3	γ(t	γ(t	NOUN
ma-227	155	4	)	)	PUNCT
ma-227	155	5	,	,	PUNCT
ma-227	155	6	imz	imz	PROPN
ma-227	155	7	≥	≥	PROPN
ma-227	155	8	0	0	NUM
ma-227	155	9	,	,	PUNCT
ma-227	155	10	−γ(t̄	−γ(t̄	PROPN
ma-227	155	11	)	)	PUNCT
ma-227	155	12	,	,	PUNCT
ma-227	155	13	imz	imz	PROPN
ma-227	155	14	<	<	X
ma-227	155	15	0.from	0.from	NUM
ma-227	155	16	the	the	DET
ma-227	155	17	properties	property	NOUN
ma-227	155	18	of	of	ADP
ma-227	155	19	the	the	DET
ma-227	155	20	poisson	poisson	PROPN
ma-227	155	21	kernel	kernel	PROPN
ma-227	155	22	for	for	ADP
ma-227	155	23	unit	unit	NOUN
ma-227	155	24	disc	disc	NOUN
ma-227	155	25	[	[	X
ma-227	155	26	2,3	2,3	NUM
ma-227	155	27	]	]	PUNCT
ma-227	155	28	,	,	PUNCT
ma-227	155	29	we	we	PRON
ma-227	155	30	have	have	VERB
ma-227	155	31	lim	lim	PROPN
ma-227	155	32	z→t	z→t	NUM
ma-227	155	33	(	(	PUNCT
ma-227	155	34	ω(z)−	ω(z)−	PROPN
ma-227	155	35	h(z	h(z	NOUN
ma-227	155	36	)	)	PUNCT
ma-227	155	37	)	)	PUNCT
ma-227	156	1	=	=	SYM
ma-227	156	2	υ(t	υ(t	NOUN
ma-227	156	3	)	)	PUNCT
ma-227	156	4	.	.	PUNCT
ma-227	157	1	in	in	ADP
ma-227	157	2	particular	particular	ADJ
ma-227	157	3	lim	lim	PROPN
ma-227	157	4	z→±1	z→±1	PROPN
ma-227	157	5	(	(	PUNCT
ma-227	157	6	ω(z)−	ω(z)−	PROPN
ma-227	157	7	h(z	h(z	NOUN
ma-227	157	8	)	)	PUNCT
ma-227	157	9	)	)	PUNCT
ma-227	158	1	=	=	SYM
ma-227	158	2	γ(±1	γ(±1	PROPN
ma-227	158	3	)	)	PUNCT
ma-227	158	4	=	=	SYM
ma-227	158	5	0	0	NUM
ma-227	158	6	,	,	PUNCT
ma-227	158	7	is	be	AUX
ma-227	158	8	seen	see	VERB
ma-227	158	9	because	because	SCONJ
ma-227	158	10	of	of	ADP
ma-227	158	11	the	the	DET
ma-227	158	12	continuity	continuity	NOUN
ma-227	158	13	of	of	ADP
ma-227	158	14	υ	υ	NOUN
ma-227	158	15	at	at	ADP
ma-227	158	16	±1	±1	NOUN
ma-227	158	17	.	.	PUNCT
ma-227	159	1	similar	similar	ADJ
ma-227	159	2	to	to	ADP
ma-227	159	3	what	what	PRON
ma-227	159	4	was	be	AUX
ma-227	159	5	done	do	VERB
ma-227	159	6	above	above	ADV
ma-227	159	7	,	,	PUNCT
ma-227	159	8	from	from	ADP
ma-227	159	9	the	the	DET
ma-227	159	10	properties	property	NOUN
ma-227	159	11	of	of	ADP
ma-227	159	12	the	the	DET
ma-227	159	13	poisson	poisson	NOUN
ma-227	159	14	kernel	kernel	PROPN
ma-227	159	15	for	for	ADP
ma-227	159	16	half	half	ADJ
ma-227	159	17	plane	plane	NOUN
ma-227	159	18	[	[	X
ma-227	159	19	2	2	NUM
ma-227	159	20	]	]	PUNCT
ma-227	159	21	,	,	PUNCT
ma-227	159	22	wehave	wehave	PROPN
ma-227	159	23	lim	lim	PROPN
ma-227	159	24	z→t	z→t	PROPN
ma-227	159	25	(	(	PUNCT
ma-227	159	26	ω(z)−	ω(z)−	PROPN
ma-227	159	27	h(z	h(z	NOUN
ma-227	159	28	)	)	PUNCT
ma-227	159	29	)	)	PUNCT
ma-227	160	1	=	=	PUNCT
ma-227	160	2	γ(t	γ(t	NOUN
ma-227	160	3	)	)	PUNCT
ma-227	160	4	.	.	PUNCT
ma-227	161	1	(	(	PUNCT
ma-227	161	2	3.6	3.6	NUM
ma-227	161	3	)	)	PUNCT
ma-227	161	4	by	by	ADP
ma-227	161	5	(	(	PUNCT
ma-227	161	6	3.4	3.4	NUM
ma-227	161	7	)	)	PUNCT
ma-227	161	8	and	and	CCONJ
ma-227	161	9	(	(	PUNCT
ma-227	161	10	3.6	3.6	NUM
ma-227	161	11	)	)	PUNCT
ma-227	161	12	,	,	PUNCT
ma-227	161	13	we	we	PRON
ma-227	161	14	have	have	VERB
ma-227	161	15	lim	lim	PROPN
ma-227	161	16	z→t	z→t	NUM
ma-227	161	17	h(z	h(z	NOUN
ma-227	161	18	)	)	PUNCT
ma-227	161	19	=	=	SYM
ma-227	162	1	0	0	NUM
ma-227	162	2	,	,	PUNCT
ma-227	162	3	t	t	PROPN
ma-227	162	4	∈	∈	PROPN
ma-227	163	1	∂m	∂m	PROPN
ma-227	163	2	.	.	PUNCT
ma-227	164	1	then	then	ADV
ma-227	164	2	,	,	PUNCT
ma-227	164	3	from	from	ADP
ma-227	164	4	the	the	DET
ma-227	164	5	maximum	maximum	ADJ
ma-227	164	6	principle	principle	NOUN
ma-227	164	7	for	for	ADP
ma-227	164	8	analytic	analytic	ADJ
ma-227	164	9	functions	function	NOUN
ma-227	164	10	h(z	h(z	NOUN
ma-227	164	11	)	)	PUNCT
ma-227	164	12	=	=	SYM
ma-227	164	13	0	0	NUM
ma-227	164	14	for	for	ADP
ma-227	164	15	z	z	PROPN
ma-227	164	16	∈	∈	PROPN
ma-227	164	17	m	m	PROPN
ma-227	164	18	,	,	PUNCT
ma-227	164	19	which	which	PRON
ma-227	164	20	is	be	AUX
ma-227	164	21	given	give	VERB
ma-227	164	22	ascondition	ascondition	NOUN
ma-227	164	23	(	(	PUNCT
ma-227	164	24	3.2	3.2	NUM
ma-227	164	25	)	)	PUNCT
ma-227	164	26	.	.	PUNCT
ma-227	165	1	conversely	conversely	ADV
ma-227	165	2	,	,	PUNCT
ma-227	165	3	if	if	SCONJ
ma-227	165	4	the	the	DET
ma-227	165	5	condition	condition	NOUN
ma-227	165	6	(	(	PUNCT
ma-227	165	7	3.2	3.2	NUM
ma-227	165	8	)	)	PUNCT
ma-227	165	9	is	be	AUX
ma-227	165	10	is	be	AUX
ma-227	165	11	satisfied	satisfied	ADJ
ma-227	165	12	,	,	PUNCT
ma-227	165	13	then	then	ADV
ma-227	165	14	,	,	PUNCT
ma-227	165	15	the	the	DET
ma-227	165	16	analytic	analytic	ADJ
ma-227	165	17	function	function	NOUN
ma-227	165	18	ω	ω	PROPN
ma-227	165	19	can	can	AUX
ma-227	165	20	be	be	AUX
ma-227	165	21	expressedas	expressedas	PROPN
ma-227	165	22	ω(z	ω(z	PROPN
ma-227	165	23	)	)	PUNCT
ma-227	166	1	=	=	PUNCT
ma-227	166	2	ω(z)−	ω(z)−	PROPN
ma-227	166	3	h(z	h(z	NOUN
ma-227	166	4	)	)	PUNCT
ma-227	166	5	=	=	SYM
ma-227	166	6	1	1	NUM
ma-227	166	7	2πi	2πi	NOUN
ma-227	166	8	∫	∫	PROPN
ma-227	166	9	∂m	∂m	PROPN
ma-227	166	10	γ(t	γ(t	PROPN
ma-227	166	11	)	)	PUNCT
ma-227	166	12	[	[	PUNCT
ma-227	166	13	1	1	NUM
ma-227	166	14	t	t	NOUN
ma-227	166	15	−	−	NOUN
ma-227	166	16	z	z	NOUN
ma-227	167	1	+	+	CCONJ
ma-227	167	2	z	z	NOUN
ma-227	167	3	tz	tz	NOUN
ma-227	167	4	−	−	PROPN
ma-227	167	5	1	1	NUM
ma-227	167	6	]	]	PUNCT
ma-227	167	7	dt	dt	X
ma-227	167	8	−	−	PROPN
ma-227	167	9	1	1	NUM
ma-227	167	10	2πi	2πi	NOUN
ma-227	167	11	∫	∫	PROPN
ma-227	167	12	∂m	∂m	PROPN
ma-227	167	13	γ(t	γ(t	PROPN
ma-227	167	14	)	)	PUNCT
ma-227	167	15	[	[	PUNCT
ma-227	167	16	1	1	NUM
ma-227	167	17	t	t	NOUN
ma-227	167	18	−	−	PROPN
ma-227	167	19	z̄	z̄	PROPN
ma-227	167	20	+	+	CCONJ
ma-227	167	21	z̄	z̄	CCONJ
ma-227	167	22	tz̄	tz̄	NOUN
ma-227	167	23	−	−	NOUN
ma-227	167	24	1	1	NUM
ma-227	167	25	]	]	PUNCT
ma-227	167	26	dt	dt	X
ma-227	167	27	=	=	SYM
ma-227	167	28	1	1	NUM
ma-227	167	29	2πi	2πi	NOUN
ma-227	167	30	∫	∫	PROPN
ma-227	167	31	∂m	∂m	PROPN
ma-227	167	32	γ(t	γ(t	PROPN
ma-227	167	33	)	)	PUNCT
ma-227	167	34	[	[	PUNCT
ma-227	167	35	1	1	NUM
ma-227	167	36	t	t	NOUN
ma-227	167	37	−	−	PROPN
ma-227	167	38	z	z	NOUN
ma-227	168	1	−	−	PROPN
ma-227	168	2	1	1	NUM
ma-227	168	3	t	t	NOUN
ma-227	168	4	−	−	PROPN
ma-227	168	5	z̄	z̄	PROPN
ma-227	169	1	+	+	CCONJ
ma-227	169	2	z	z	NOUN
ma-227	169	3	tz	tz	NOUN
ma-227	169	4	−	−	NUM
ma-227	169	5	1	1	NUM
ma-227	169	6	−	−	PROPN
ma-227	169	7	z̄	z̄	NOUN
ma-227	169	8	tz̄	tz̄	NOUN
ma-227	169	9	−	−	NOUN
ma-227	169	10	1	1	NUM
ma-227	169	11	]	]	PUNCT
ma-227	169	12	dt	dt	X
ma-227	169	13	.	.	PUNCT
ma-227	170	1	hence	hence	ADV
ma-227	170	2	,	,	PUNCT
ma-227	170	3	lim	lim	PROPN
ma-227	170	4	z→t	z→t	NUM
ma-227	170	5	ω(z	ω(z	PROPN
ma-227	170	6	)	)	PUNCT
ma-227	170	7	=	=	PUNCT
ma-227	171	1	γ(t	γ(t	NOUN
ma-227	171	2	)	)	PUNCT
ma-227	171	3	,	,	PUNCT
ma-227	171	4	t	t	PROPN
ma-227	171	5	∈	∈	PROPN
ma-227	171	6	∂m	∂m	PROPN
ma-227	171	7	.	.	PUNCT
ma-227	172	1	(	(	PUNCT
ma-227	172	2	3.7	3.7	NUM
ma-227	172	3	)	)	PUNCT
ma-227	172	4	follows	follow	VERB
ma-227	172	5	again	again	ADV
ma-227	172	6	from	from	ADP
ma-227	172	7	the	the	DET
ma-227	172	8	properties	property	NOUN
ma-227	172	9	of	of	ADP
ma-227	172	10	the	the	DET
ma-227	172	11	poisson	poisson	PROPN
ma-227	172	12	kernel	kernel	PROPN
ma-227	172	13	.	.	PUNCT
ma-227	173	1	�	�	PROPN
ma-227	173	2	https://doi.org/10.28924/ada/ma.4.15	https://doi.org/10.28924/ada/ma.4.15	PROPN
ma-227	173	3	eur	eur	PROPN
ma-227	173	4	.	.	PUNCT
ma-227	174	1	j.	j.	PROPN
ma-227	174	2	math	math	PROPN
ma-227	174	3	.	.	PUNCT
ma-227	175	1	anal	anal	PROPN
ma-227	175	2	.	.	PUNCT
ma-227	176	1	10.28924	10.28924	NUM
ma-227	176	2	/	/	SYM
ma-227	176	3	ada	ada	PROPN
ma-227	176	4	/	/	SYM
ma-227	176	5	ma.4.15	ma.4.15	PROPN
ma-227	176	6	7	7	NUM
ma-227	176	7	in	in	ADP
ma-227	176	8	the	the	DET
ma-227	176	9	next	next	ADJ
ma-227	176	10	stage	stage	NOUN
ma-227	176	11	,	,	PUNCT
ma-227	176	12	we	we	PRON
ma-227	176	13	investigate	investigate	VERB
ma-227	176	14	the	the	DET
ma-227	176	15	dirichlet	dirichlet	PROPN
ma-227	176	16	problem	problem	NOUN
ma-227	176	17	for	for	ADP
ma-227	176	18	the	the	DET
ma-227	176	19	inhomogeneous	inhomogeneous	ADJ
ma-227	176	20	cauchy	cauchy	NOUN
ma-227	176	21	–	–	PUNCT
ma-227	176	22	riemannequation	riemannequation	NOUN
ma-227	176	23	.	.	PUNCT
ma-227	177	1	to	to	PART
ma-227	177	2	solve	solve	VERB
ma-227	177	3	this	this	DET
ma-227	177	4	problem	problem	NOUN
ma-227	177	5	,	,	PUNCT
ma-227	177	6	we	we	PRON
ma-227	177	7	reduce	reduce	VERB
ma-227	177	8	the	the	DET
ma-227	177	9	inhomogeneous	inhomogeneous	ADJ
ma-227	177	10	problem	problem	NOUN
ma-227	177	11	into	into	ADP
ma-227	177	12	a	a	DET
ma-227	177	13	homogeneous	homogeneous	ADJ
ma-227	177	14	one	one	NOUN
ma-227	177	15	,	,	PUNCT
ma-227	177	16	using	use	VERB
ma-227	177	17	definition	definition	NOUN
ma-227	177	18	and	and	CCONJ
ma-227	177	19	properties	property	NOUN
ma-227	177	20	of	of	ADP
ma-227	177	21	the	the	DET
ma-227	177	22	pompeiu	pompeiu	NOUN
ma-227	177	23	operator	operator	NOUN
ma-227	177	24	,	,	PUNCT
ma-227	177	25	and	and	CCONJ
ma-227	177	26	then	then	ADV
ma-227	177	27	find	find	VERB
ma-227	177	28	a	a	DET
ma-227	177	29	solution	solution	NOUN
ma-227	177	30	for	for	ADP
ma-227	177	31	it	it	PRON
ma-227	177	32	using	use	VERB
ma-227	177	33	theprevious	theprevious	ADJ
ma-227	177	34	theorem	theorem	VERB
ma-227	177	35	.	.	PUNCT
ma-227	177	36	theorem	theorem	PROPN
ma-227	177	37	3.2	3.2	NUM
ma-227	177	38	.	.	PUNCT
ma-227	178	1	the	the	DET
ma-227	178	2	dirichlet	dirichlet	PROPN
ma-227	178	3	boundary	boundary	PROPN
ma-227	178	4	value	value	NOUN
ma-227	178	5	problem	problem	NOUN
ma-227	178	6	for	for	ADP
ma-227	178	7	the	the	DET
ma-227	178	8	inhomogeneous	inhomogeneous	ADJ
ma-227	178	9	cauchy	cauchy	PROPN
ma-227	178	10	–	–	PUNCT
ma-227	178	11	riemann	riemann	PROPN
ma-227	178	12	equation	equation	NOUN
ma-227	178	13	ωz̄	ωz̄	NOUN
ma-227	179	1	=	=	PUNCT
ma-227	179	2	f	f	X
ma-227	179	3	(	(	PUNCT
ma-227	179	4	z	z	NOUN
ma-227	179	5	)	)	PUNCT
ma-227	179	6	,	,	PUNCT
ma-227	179	7	z	z	PROPN
ma-227	179	8	∈	∈	PROPN
ma-227	179	9	m	m	PROPN
ma-227	179	10	,	,	PUNCT
ma-227	179	11	f	f	PROPN
ma-227	179	12	∈	∈	PROPN
ma-227	179	13	lp(m;c	lp(m;c	NOUN
ma-227	179	14	)	)	PUNCT
ma-227	179	15	,	,	PUNCT
ma-227	179	16	p	p	X
ma-227	179	17	>	>	X
ma-227	179	18	2	2	NUM
ma-227	179	19	,	,	PUNCT
ma-227	179	20	ω	ω	NOUN
ma-227	179	21	=	=	SYM
ma-227	179	22	γ	γ	PROPN
ma-227	179	23	,	,	PUNCT
ma-227	179	24	on	on	ADP
ma-227	179	25	∂m	∂m	PROPN
ma-227	179	26	,	,	PUNCT
ma-227	179	27	γ	γ	PROPN
ma-227	179	28	∈	∈	PROPN
ma-227	179	29	c(∂m;c	c(∂m;c	NOUN
ma-227	179	30	)	)	PUNCT
ma-227	179	31	,	,	PUNCT
ma-227	179	32	(	(	PUNCT
ma-227	179	33	3.8	3.8	NUM
ma-227	179	34	)	)	PUNCT
ma-227	179	35	is	be	AUX
ma-227	179	36	solvable	solvable	ADJ
ma-227	179	37	if	if	SCONJ
ma-227	179	38	and	and	CCONJ
ma-227	179	39	only	only	ADV
ma-227	179	40	if	if	SCONJ
ma-227	179	41	for	for	ADP
ma-227	179	42	z	z	PROPN
ma-227	179	43	∈	∈	PROPN
ma-227	179	44	m	m	PROPN
ma-227	179	45	,	,	PUNCT
ma-227	179	46	1	1	NUM
ma-227	179	47	2πi	2πi	NOUN
ma-227	179	48	∫	∫	PROPN
ma-227	179	49	∂m	∂m	PROPN
ma-227	180	1	γ(t	γ(t	PROPN
ma-227	180	2	)	)	PUNCT
ma-227	181	1	[	[	PUNCT
ma-227	181	2	1	1	NUM
ma-227	181	3	t	t	NOUN
ma-227	181	4	−	−	PROPN
ma-227	181	5	z̄	z̄	PROPN
ma-227	181	6	+	+	CCONJ
ma-227	181	7	z̄	z̄	CCONJ
ma-227	181	8	tz̄	tz̄	NOUN
ma-227	181	9	−	−	NOUN
ma-227	181	10	1	1	NUM
ma-227	181	11	]	]	PUNCT
ma-227	181	12	dt	dt	X
ma-227	181	13	=	=	SYM
ma-227	181	14	1	1	NUM
ma-227	181	15	π	π	PROPN
ma-227	181	16	∫	∫	PROPN
ma-227	181	17	m	m	PROPN
ma-227	181	18	f	f	PROPN
ma-227	181	19	(	(	PUNCT
ma-227	181	20	t	t	PROPN
ma-227	181	21	)	)	PUNCT
ma-227	181	22	[	[	PUNCT
ma-227	181	23	1	1	NUM
ma-227	181	24	ζ	ζ	NOUN
ma-227	181	25	−	−	PROPN
ma-227	181	26	z̄	z̄	CCONJ
ma-227	181	27	+	+	CCONJ
ma-227	181	28	z̄	z̄	CCONJ
ma-227	181	29	tz̄	tz̄	NOUN
ma-227	181	30	−	−	NOUN
ma-227	181	31	1	1	NUM
ma-227	181	32	]	]	X
ma-227	181	33	dξdη	dξdη	PROPN
ma-227	181	34	,	,	PUNCT
ma-227	181	35	(	(	PUNCT
ma-227	181	36	3.9	3.9	NUM
ma-227	181	37	)	)	PUNCT
ma-227	181	38	and	and	CCONJ
ma-227	181	39	its	its	PRON
ma-227	181	40	solution	solution	NOUN
ma-227	181	41	can	can	AUX
ma-227	181	42	be	be	AUX
ma-227	181	43	uniquely	uniquely	ADV
ma-227	181	44	expressed	express	VERB
ma-227	181	45	as	as	ADP
ma-227	181	46	ω(z	ω(z	PROPN
ma-227	181	47	)	)	PUNCT
ma-227	181	48	=	=	SYM
ma-227	181	49	1	1	NUM
ma-227	181	50	2πi	2πi	NOUN
ma-227	181	51	∫	∫	PROPN
ma-227	181	52	∂m	∂m	PROPN
ma-227	181	53	γ(t	γ(t	PROPN
ma-227	181	54	)	)	PUNCT
ma-227	182	1	[	[	PUNCT
ma-227	182	2	1	1	NUM
ma-227	182	3	t	t	NOUN
ma-227	182	4	−	−	NOUN
ma-227	182	5	z	z	NOUN
ma-227	183	1	+	+	CCONJ
ma-227	183	2	z	z	NOUN
ma-227	183	3	tz	tz	NOUN
ma-227	183	4	−	−	PROPN
ma-227	183	5	1	1	NUM
ma-227	183	6	]	]	PUNCT
ma-227	183	7	dt	dt	X
ma-227	183	8	−	−	PROPN
ma-227	183	9	1	1	NUM
ma-227	183	10	π	π	NOUN
ma-227	183	11	∫	∫	PROPN
ma-227	183	12	m	m	PROPN
ma-227	183	13	f	f	PROPN
ma-227	183	14	(	(	PUNCT
ma-227	183	15	t	t	PROPN
ma-227	183	16	)	)	PUNCT
ma-227	183	17	[	[	PUNCT
ma-227	183	18	1	1	NUM
ma-227	183	19	t	t	NOUN
ma-227	183	20	−	−	NOUN
ma-227	183	21	z	z	NOUN
ma-227	184	1	+	+	CCONJ
ma-227	184	2	z	z	NOUN
ma-227	184	3	tz	tz	NOUN
ma-227	184	4	−	−	PROPN
ma-227	184	5	1	1	NUM
ma-227	184	6	]	]	PUNCT
ma-227	184	7	dξdη	dξdη	NOUN
ma-227	184	8	.	.	PUNCT
ma-227	185	1	(	(	PUNCT
ma-227	185	2	3.10	3.10	NUM
ma-227	185	3	)	)	PUNCT
ma-227	186	1	where	where	SCONJ
ma-227	186	2	t	t	NOUN
ma-227	186	3	=	=	SYM
ma-227	186	4	ξ	ξ	PROPN
ma-227	186	5	+	+	NUM
ma-227	186	6	iη	iη	NOUN
ma-227	186	7	.	.	PUNCT
ma-227	187	1	proof	proof	NOUN
ma-227	187	2	.	.	PUNCT
ma-227	188	1	by	by	ADP
ma-227	188	2	the	the	DET
ma-227	188	3	theorem	theorem	NOUN
ma-227	188	4	2.1	2.1	NUM
ma-227	188	5	,	,	PUNCT
ma-227	188	6	if	if	SCONJ
ma-227	188	7	the	the	DET
ma-227	188	8	dirichlet	dirichlet	PROPN
ma-227	188	9	problem	problem	NOUN
ma-227	188	10	(	(	PUNCT
ma-227	188	11	3.8	3.8	NUM
ma-227	188	12	)	)	PUNCT
ma-227	188	13	is	be	AUX
ma-227	188	14	solvable	solvable	ADJ
ma-227	188	15	,	,	PUNCT
ma-227	188	16	its	its	PRON
ma-227	188	17	can	can	AUX
ma-227	188	18	be	be	AUX
ma-227	188	19	expressed	express	VERB
ma-227	188	20	in	in	ADP
ma-227	188	21	theform	theform	NOUN
ma-227	188	22	of	of	ADP
ma-227	188	23	(	(	PUNCT
ma-227	188	24	3.10	3.10	NUM
ma-227	188	25	)	)	PUNCT
ma-227	188	26	.	.	PUNCT
ma-227	189	1	let	let	VERB
ma-227	189	2	ϕ(z	ϕ(z	NOUN
ma-227	189	3	)	)	PUNCT
ma-227	190	1	=	=	PUNCT
ma-227	190	2	ω(z)−	ω(z)−	PROPN
ma-227	190	3	t	t	NOUN
ma-227	190	4	f	f	X
ma-227	190	5	(	(	PUNCT
ma-227	190	6	z	z	NOUN
ma-227	190	7	)	)	PUNCT
ma-227	190	8	,	,	PUNCT
ma-227	190	9	by	by	ADP
ma-227	190	10	applying	apply	VERB
ma-227	190	11	the	the	DET
ma-227	190	12	∂z̄	∂z̄	PROPN
ma-227	190	13	operator	operator	NOUN
ma-227	190	14	to	to	ADP
ma-227	190	15	the	the	DET
ma-227	190	16	function	function	NOUN
ma-227	190	17	’	'	PUNCT
ma-227	190	18	we	we	PRON
ma-227	190	19	have	have	VERB
ma-227	190	20	,	,	PUNCT
ma-227	190	21	∂z̄ϕ	∂z̄ϕ	ADJ
ma-227	190	22	=	=	SYM
ma-227	190	23	∂z̄ω	∂z̄ω	PROPN
ma-227	190	24	−	−	PROPN
ma-227	190	25	∂z̄t	∂z̄t	NOUN
ma-227	190	26	f	f	PROPN
ma-227	190	27	⇒	⇒	PROPN
ma-227	190	28	∂z̄ϕ	∂z̄ϕ	VERB
ma-227	190	29	=	=	PUNCT
ma-227	190	30	f	f	PROPN
ma-227	190	31	−	−	PROPN
ma-227	190	32	f	f	NOUN
ma-227	190	33	=	=	SYM
ma-227	190	34	0	0	PROPN
ma-227	190	35	,	,	PUNCT
ma-227	190	36	ϕ	ϕ	X
ma-227	191	1	=	=	SYM
ma-227	191	2	ω	ω	PROPN
ma-227	191	3	−	−	NOUN
ma-227	191	4	t	t	PROPN
ma-227	191	5	f	f	PROPN
ma-227	191	6	⇒	⇒	PROPN
ma-227	191	7	ϕ	ϕ	X
ma-227	191	8	=	=	PUNCT
ma-227	191	9	γ	γ	X
ma-227	191	10	−	−	PROPN
ma-227	191	11	t	t	PROPN
ma-227	191	12	f	f	PROPN
ma-227	191	13	.	.	PUNCT
ma-227	192	1	then	then	ADV
ma-227	192	2	consider	consider	VERB
ma-227	192	3	the	the	DET
ma-227	192	4	homogeneous	homogeneous	ADJ
ma-227	192	5	dirichlet	dirichlet	PROPN
ma-227	192	6	problem	problem	NOUN
ma-227	192	7	ϕz̄	ϕz̄	PROPN
ma-227	193	1	=	=	NOUN
ma-227	193	2	0	0	NUM
ma-227	193	3	,	,	PUNCT
ma-227	193	4	in	in	ADP
ma-227	193	5	z	z	PROPN
ma-227	193	6	∈	∈	PROPN
ma-227	193	7	m	m	PROPN
ma-227	193	8	,	,	PUNCT
ma-227	193	9	ϕ	ϕ	X
ma-227	193	10	=	=	PUNCT
ma-227	193	11	γ	γ	X
ma-227	193	12	−	−	PROPN
ma-227	193	13	t	t	PROPN
ma-227	193	14	f	f	PROPN
ma-227	193	15	,	,	PUNCT
ma-227	193	16	on	on	ADP
ma-227	193	17	∂m	∂m	PROPN
ma-227	193	18	.	.	PUNCT
ma-227	194	1	(	(	PUNCT
ma-227	194	2	3.11	3.11	NUM
ma-227	194	3	)	)	PUNCT
ma-227	194	4	which	which	PRON
ma-227	194	5	is	be	AUX
ma-227	194	6	equivalent	equivalent	ADJ
ma-227	194	7	to	to	ADP
ma-227	194	8	equation	equation	NOUN
ma-227	194	9	(	(	PUNCT
ma-227	194	10	3.11	3.11	NUM
ma-227	194	11	)	)	PUNCT
ma-227	194	12	by	by	ADP
ma-227	194	13	the	the	DET
ma-227	194	14	theorem	theorem	NOUN
ma-227	194	15	3.2	3.2	NUM
ma-227	194	16	the	the	DET
ma-227	194	17	solvability	solvability	NOUN
ma-227	194	18	condition	condition	NOUN
ma-227	194	19	for	for	ADP
ma-227	194	20	equation(3.14	equation(3.14	NOUN
ma-227	194	21	)	)	PUNCT
ma-227	194	22	is	be	AUX
ma-227	194	23	1	1	NUM
ma-227	194	24	2πi	2πi	NOUN
ma-227	194	25	∫	∫	PROPN
ma-227	194	26	∂m	∂m	PROPN
ma-227	195	1	(	(	PUNCT
ma-227	195	2	γ(t)−	γ(t)−	PROPN
ma-227	195	3	t	t	PROPN
ma-227	195	4	f	f	PROPN
ma-227	195	5	(	(	PUNCT
ma-227	195	6	t	t	PROPN
ma-227	195	7	)	)	PUNCT
ma-227	195	8	)	)	PUNCT
ma-227	196	1	[	[	PUNCT
ma-227	196	2	1	1	NUM
ma-227	196	3	t	t	NOUN
ma-227	196	4	−	−	PROPN
ma-227	196	5	z̄	z̄	PROPN
ma-227	196	6	+	+	CCONJ
ma-227	196	7	z̄	z̄	CCONJ
ma-227	196	8	tz̄	tz̄	NOUN
ma-227	196	9	−	−	NOUN
ma-227	196	10	1	1	NUM
ma-227	196	11	]	]	PUNCT
ma-227	196	12	dt	dt	X
ma-227	196	13	=	=	SYM
ma-227	196	14	0	0	PROPN
ma-227	196	15	,	,	PUNCT
ma-227	196	16	using	use	VERB
ma-227	196	17	the	the	DET
ma-227	196	18	properties	property	NOUN
ma-227	196	19	of	of	ADP
ma-227	196	20	the	the	DET
ma-227	196	21	integral	integral	ADJ
ma-227	196	22	operator	operator	NOUN
ma-227	196	23	1	1	NUM
ma-227	196	24	2πi	2πi	NOUN
ma-227	196	25	∫	∫	PROPN
ma-227	197	1	∂m	∂m	PROPN
ma-227	197	2	t	t	PROPN
ma-227	197	3	f	f	PROPN
ma-227	197	4	(	(	PUNCT
ma-227	197	5	t	t	PROPN
ma-227	197	6	)	)	PUNCT
ma-227	198	1	[	[	PUNCT
ma-227	198	2	1	1	NUM
ma-227	198	3	t	t	NOUN
ma-227	198	4	−	−	PROPN
ma-227	198	5	z̄	z̄	PROPN
ma-227	198	6	+	+	CCONJ
ma-227	198	7	z̄	z̄	CCONJ
ma-227	198	8	tz̄	tz̄	NOUN
ma-227	198	9	−	−	NOUN
ma-227	198	10	1	1	NUM
ma-227	198	11	]	]	PUNCT
ma-227	198	12	dt	dt	X
ma-227	199	1	=	=	SYM
ma-227	199	2	1	1	NUM
ma-227	199	3	π	π	PROPN
ma-227	199	4	∫	∫	PROPN
ma-227	199	5	m	m	PROPN
ma-227	199	6	f	f	PROPN
ma-227	199	7	(	(	PUNCT
ma-227	199	8	t̃	t̃	PROPN
ma-227	199	9	)	)	PUNCT
ma-227	199	10	1	1	NUM
ma-227	199	11	2πi	2πi	NOUN
ma-227	199	12	∫	∫	PROPN
ma-227	199	13	∂m	∂m	X
ma-227	200	1	[	[	PUNCT
ma-227	200	2	1	1	NUM
ma-227	200	3	t	t	PROPN
ma-227	200	4	−	−	PROPN
ma-227	200	5	z̄	z̄	PROPN
ma-227	200	6	+	+	CCONJ
ma-227	200	7	z̄	z̄	CCONJ
ma-227	200	8	tz̄	tz̄	NOUN
ma-227	200	9	−	−	NOUN
ma-227	200	10	1	1	NUM
ma-227	200	11	]	]	PUNCT
ma-227	200	12	dt	dt	X
ma-227	200	13	t	t	PROPN
ma-227	201	1	−	−	PROPN
ma-227	201	2	t̃	t̃	PROPN
ma-227	201	3	d	d	PROPN
ma-227	201	4	ξ̃dη̃	ξ̃dη̃	NOUN
ma-227	201	5	=	=	SYM
ma-227	201	6	1	1	NUM
ma-227	201	7	π	π	NOUN
ma-227	201	8	∫	∫	PROPN
ma-227	202	1	m	m	PROPN
ma-227	202	2	f	f	PROPN
ma-227	202	3	(	(	PUNCT
ma-227	202	4	t̃	t̃	PROPN
ma-227	202	5	)	)	PUNCT
ma-227	202	6	[	[	PUNCT
ma-227	202	7	1	1	NUM
ma-227	202	8	t̃	t̃	PROPN
ma-227	202	9	−	−	PROPN
ma-227	202	10	z̄	z̄	NOUN
ma-227	202	11	+	+	CCONJ
ma-227	202	12	z̄	z̄	X
ma-227	202	13	t̃	t̃	PROPN
ma-227	202	14	z̄	z̄	NOUN
ma-227	202	15	−	−	ADP
ma-227	202	16	1	1	NUM
ma-227	202	17	]	]	PUNCT
ma-227	202	18	dξ̃dη̃.	dξ̃dη̃.	X
ma-227	202	19	which	which	PRON
ma-227	202	20	is	be	AUX
ma-227	202	21	just	just	ADV
ma-227	202	22	condition	condition	NOUN
ma-227	202	23	(	(	PUNCT
ma-227	202	24	3.9	3.9	NUM
ma-227	202	25	)	)	PUNCT
ma-227	202	26	.	.	PUNCT
ma-227	203	1	https://doi.org/10.28924/ada/ma.4.15	https://doi.org/10.28924/ada/ma.4.15	AUX
ma-227	203	2	eur	eur	PROPN
ma-227	203	3	.	.	PUNCT
ma-227	204	1	j.	j.	PROPN
ma-227	204	2	math	math	PROPN
ma-227	204	3	.	.	PUNCT
ma-227	205	1	anal	anal	PROPN
ma-227	205	2	.	.	PUNCT
ma-227	206	1	10.28924	10.28924	NUM
ma-227	206	2	/	/	SYM
ma-227	206	3	ada	ada	PROPN
ma-227	206	4	/	/	SYM
ma-227	206	5	ma.4.15	ma.4.15	PROPN
ma-227	206	6	8on	8on	NOUN
ma-227	206	7	the	the	DET
ma-227	206	8	other	other	ADJ
ma-227	206	9	hand	hand	NOUN
ma-227	206	10	,	,	PUNCT
ma-227	206	11	if	if	SCONJ
ma-227	206	12	the	the	DET
ma-227	206	13	condition	condition	NOUN
ma-227	206	14	of	of	ADP
ma-227	206	15	solvability	solvability	NOUN
ma-227	206	16	(	(	PUNCT
ma-227	206	17	3.9	3.9	NUM
ma-227	206	18	)	)	PUNCT
ma-227	206	19	is	be	AUX
ma-227	206	20	satisfied	satisfied	ADJ
ma-227	206	21	,	,	PUNCT
ma-227	206	22	then	then	ADV
ma-227	206	23	(	(	PUNCT
ma-227	206	24	3.10	3.10	NUM
ma-227	206	25	)	)	PUNCT
ma-227	206	26	can	can	AUX
ma-227	206	27	be	be	AUX
ma-227	206	28	expressedas	expressedas	PROPN
ma-227	206	29	follows	follow	VERB
ma-227	206	30	.	.	PUNCT
ma-227	207	1	ω(z	ω(z	PUNCT
ma-227	207	2	)	)	PUNCT
ma-227	207	3	=	=	SYM
ma-227	207	4	1	1	NUM
ma-227	207	5	2πi	2πi	NOUN
ma-227	207	6	∫	∫	PROPN
ma-227	207	7	∂m	∂m	PROPN
ma-227	207	8	γ(z	γ(z	PROPN
ma-227	207	9	)	)	PUNCT
ma-227	207	10	[	[	PUNCT
ma-227	207	11	1	1	NUM
ma-227	207	12	t	t	NOUN
ma-227	207	13	−	−	NOUN
ma-227	207	14	z	z	NOUN
ma-227	208	1	+	+	CCONJ
ma-227	208	2	z	z	NOUN
ma-227	208	3	tz	tz	NOUN
ma-227	208	4	−	−	NUM
ma-227	208	5	1	1	NUM
ma-227	208	6	−	−	PROPN
ma-227	208	7	1	1	NUM
ma-227	208	8	t	t	NOUN
ma-227	208	9	−	−	PROPN
ma-227	208	10	z̄	z̄	CCONJ
ma-227	208	11	−	−	PRON
ma-227	208	12	z̄	z̄	NOUN
ma-227	208	13	tz̄	tz̄	NOUN
ma-227	208	14	−	−	NOUN
ma-227	208	15	1	1	NUM
ma-227	208	16	]	]	PUNCT
ma-227	208	17	dt	dt	X
ma-227	208	18	.	.	PUNCT
ma-227	209	1	−	−	NOUN
ma-227	209	2	1	1	NUM
ma-227	210	1	π	π	NOUN
ma-227	210	2	∫	∫	PROPN
ma-227	210	3	m	m	PROPN
ma-227	210	4	f	f	PROPN
ma-227	210	5	(	(	PUNCT
ma-227	210	6	z	z	NOUN
ma-227	210	7	)	)	PUNCT
ma-227	210	8	[	[	PUNCT
ma-227	210	9	1	1	NUM
ma-227	210	10	t	t	NOUN
ma-227	210	11	−	−	NOUN
ma-227	210	12	z	z	NOUN
ma-227	211	1	+	+	CCONJ
ma-227	211	2	z	z	NOUN
ma-227	211	3	tz	tz	NOUN
ma-227	211	4	−	−	NUM
ma-227	211	5	1	1	NUM
ma-227	211	6	−	−	PROPN
ma-227	211	7	1	1	NUM
ma-227	211	8	t	t	NOUN
ma-227	211	9	−	−	PROPN
ma-227	211	10	z̄	z̄	CCONJ
ma-227	211	11	−	−	PRON
ma-227	211	12	z̄	z̄	NOUN
ma-227	211	13	tz̄	tz̄	NOUN
ma-227	211	14	−	−	NOUN
ma-227	211	15	1	1	NUM
ma-227	211	16	]	]	PUNCT
ma-227	211	17	dξdη	dξdη	NOUN
ma-227	211	18	.	.	PUNCT
ma-227	212	1	(	(	PUNCT
ma-227	212	2	3.12	3.12	NUM
ma-227	212	3	)	)	PUNCT
ma-227	212	4	since	since	SCONJ
ma-227	212	5	the	the	DET
ma-227	212	6	area	area	NOUN
ma-227	212	7	integral	integral	ADJ
ma-227	212	8	tends	tend	VERB
ma-227	212	9	to	to	ADP
ma-227	212	10	0	0	NUM
ma-227	212	11	as	as	ADP
ma-227	212	12	z	z	PROPN
ma-227	212	13	→	→	SYM
ma-227	212	14	t	t	PROPN
ma-227	212	15	∈	∈	PROPN
ma-227	212	16	∂m	∂m	PROPN
ma-227	212	17	,	,	PUNCT
ma-227	212	18	by	by	ADP
ma-227	212	19	the	the	DET
ma-227	212	20	proof	proof	NOUN
ma-227	212	21	of	of	ADP
ma-227	212	22	theorem	theorem	NOUN
ma-227	212	23	(	(	PUNCT
ma-227	212	24	3.2	3.2	NUM
ma-227	212	25	)	)	PUNCT
ma-227	212	26	,	,	PUNCT
ma-227	212	27	(	(	PUNCT
ma-227	212	28	3.12	3.12	NUM
ma-227	212	29	)	)	PUNCT
ma-227	212	30	impliesthat	impliesthat	NOUN
ma-227	212	31	lim	lim	PROPN
ma-227	212	32	z→t	z→t	NUM
ma-227	212	33	ω(z	ω(z	PROPN
ma-227	212	34	)	)	PUNCT
ma-227	212	35	=	=	PUNCT
ma-227	213	1	γ(t	γ(t	NOUN
ma-227	213	2	)	)	PUNCT
ma-227	213	3	,	,	PUNCT
ma-227	213	4	t	t	PROPN
ma-227	213	5	∈	∈	PROPN
ma-227	213	6	∂m.now	∂m.now	PROPN
ma-227	213	7	,	,	PUNCT
ma-227	213	8	we	we	PRON
ma-227	213	9	are	be	AUX
ma-227	213	10	going	go	VERB
ma-227	213	11	to	to	PART
ma-227	213	12	investigate	investigate	VERB
ma-227	213	13	the	the	DET
ma-227	213	14	uniqueness	uniqueness	NOUN
ma-227	213	15	of	of	ADP
ma-227	213	16	the	the	DET
ma-227	213	17	dirichlet	dirichlet	PROPN
ma-227	213	18	problem	problem	NOUN
ma-227	213	19	solution	solution	NOUN
ma-227	213	20	.	.	PUNCT
ma-227	214	1	assume	assume	VERB
ma-227	214	2	that	that	SCONJ
ma-227	214	3	ωand	ωand	ADJ
ma-227	214	4	w	w	NOUN
ma-227	214	5	are	be	AUX
ma-227	214	6	two	two	NUM
ma-227	214	7	solutions	solution	NOUN
ma-227	214	8	to	to	ADP
ma-227	214	9	the	the	DET
ma-227	214	10	dirichlet	dirichlet	PROPN
ma-227	214	11	problem	problem	NOUN
ma-227	214	12	,	,	PUNCT
ma-227	214	13	therefore	therefore	ADV
ma-227	214	14	we	we	PRON
ma-227	214	15	have	have	VERB
ma-227	214	16	ωz̄	ωz̄	NOUN
ma-227	214	17	=	=	SYM
ma-227	214	18	f	f	PROPN
ma-227	214	19	,	,	PUNCT
ma-227	214	20	in	in	ADP
ma-227	214	21	z	z	PROPN
ma-227	214	22	∈	∈	PROPN
ma-227	214	23	m	m	PROPN
ma-227	214	24	,	,	PUNCT
ma-227	215	1	ω	ω	PROPN
ma-227	215	2	=	=	PUNCT
ma-227	215	3	γ	γ	X
ma-227	215	4	on	on	ADP
ma-227	215	5	∂m	∂m	PROPN
ma-227	215	6	,	,	PUNCT
ma-227	215	7	wz̄	wz̄	NOUN
ma-227	215	8	=	=	SYM
ma-227	215	9	f	f	PROPN
ma-227	215	10	,	,	PUNCT
ma-227	215	11	in	in	ADP
ma-227	215	12	z	z	PROPN
ma-227	215	13	∈	∈	PROPN
ma-227	215	14	m	m	PROPN
ma-227	215	15	,	,	PUNCT
ma-227	215	16	w	w	PROPN
ma-227	215	17	=	=	SYM
ma-227	215	18	γ	γ	PROPN
ma-227	215	19	,	,	PUNCT
ma-227	215	20	on	on	ADP
ma-227	215	21	∂m.by	∂m.by	PUNCT
ma-227	215	22	subtracting	subtract	VERB
ma-227	215	23	the	the	DET
ma-227	215	24	above	above	ADJ
ma-227	215	25	two	two	NUM
ma-227	215	26	relations	relation	NOUN
ma-227	215	27	,	,	PUNCT
ma-227	215	28	we	we	PRON
ma-227	215	29	conclude	conclude	VERB
ma-227	215	30	that	that	SCONJ
ma-227	215	31	(	(	PUNCT
ma-227	215	32	ω	ω	NUM
ma-227	215	33	−	−	NOUN
ma-227	215	34	w)z̄	w)z̄	NOUN
ma-227	215	35	=	=	SYM
ma-227	215	36	0	0	NUM
ma-227	215	37	,	,	PUNCT
ma-227	215	38	in	in	ADP
ma-227	215	39	m	m	PROPN
ma-227	215	40	ω	ω	NOUN
ma-227	215	41	−	−	PROPN
ma-227	215	42	w	w	NOUN
ma-227	215	43	=	=	NOUN
ma-227	215	44	0	0	PROPN
ma-227	215	45	.	.	PUNCT
ma-227	216	1	in	in	ADP
ma-227	216	2	m	m	PROPN
ma-227	216	3	,	,	PUNCT
ma-227	216	4	this	this	PRON
ma-227	216	5	completes	complete	VERB
ma-227	216	6	the	the	DET
ma-227	216	7	proof	proof	NOUN
ma-227	216	8	.	.	PUNCT
ma-227	217	1	�	�	PROPN
ma-227	217	2	acknowledgments	acknowledgment	NOUN
ma-227	217	3	the	the	DET
ma-227	217	4	authors	author	NOUN
ma-227	217	5	would	would	AUX
ma-227	217	6	like	like	VERB
ma-227	217	7	to	to	PART
ma-227	217	8	express	express	VERB
ma-227	217	9	their	their	PRON
ma-227	217	10	sincere	sincere	ADJ
ma-227	217	11	gratitude	gratitude	NOUN
ma-227	217	12	to	to	ADP
ma-227	217	13	the	the	DET
ma-227	217	14	editor	editor	NOUN
ma-227	217	15	in	in	ADP
ma-227	217	16	chief	chief	NOUN
ma-227	217	17	,	,	PUNCT
ma-227	217	18	associate	associate	ADJ
ma-227	217	19	editorand	editorand	NOUN
ma-227	217	20	referees	referee	NOUN
ma-227	217	21	for	for	ADP
ma-227	217	22	their	their	PRON
ma-227	217	23	valuable	valuable	ADJ
ma-227	217	24	comments	comment	NOUN
ma-227	217	25	that	that	PRON
ma-227	217	26	led	lead	VERB
ma-227	217	27	to	to	ADP
ma-227	217	28	considerable	considerable	ADJ
ma-227	217	29	improvement	improvement	NOUN
ma-227	217	30	of	of	ADP
ma-227	217	31	the	the	DET
ma-227	217	32	article	article	NOUN
ma-227	217	33	.	.	PUNCT
ma-227	218	1	declarations	declaration	NOUN
ma-227	218	2	there	there	PRON
ma-227	218	3	is	be	VERB
ma-227	218	4	no	no	DET
ma-227	218	5	conflict	conflict	NOUN
ma-227	218	6	of	of	ADP
ma-227	218	7	interest	interest	NOUN
ma-227	218	8	related	relate	VERB
ma-227	218	9	to	to	ADP
ma-227	218	10	the	the	DET
ma-227	218	11	present	present	ADJ
ma-227	218	12	research	research	NOUN
ma-227	218	13	.	.	PUNCT
ma-227	219	1	the	the	DET
ma-227	219	2	work	work	NOUN
ma-227	219	3	has	have	AUX
ma-227	219	4	not	not	PART
ma-227	219	5	been	be	AUX
ma-227	219	6	publishedbefore	publishedbefore	ADJ
ma-227	219	7	and	and	CCONJ
ma-227	219	8	is	be	AUX
ma-227	219	9	not	not	PART
ma-227	219	10	under	under	ADP
ma-227	219	11	consideration	consideration	NOUN
ma-227	219	12	elsewhere	elsewhere	ADV
ma-227	219	13	.	.	PUNCT
ma-227	220	1	this	this	DET
ma-227	220	2	research	research	NOUN
ma-227	220	3	received	receive	VERB
ma-227	220	4	no	no	DET
ma-227	220	5	particular	particular	ADJ
ma-227	220	6	grant	grant	NOUN
ma-227	220	7	fromany	fromany	NOUN
ma-227	220	8	funding	funding	NOUN
ma-227	220	9	agency	agency	NOUN
ma-227	220	10	.	.	PUNCT
ma-227	221	1	references	reference	NOUN
ma-227	221	2	[	[	X
ma-227	221	3	1	1	NUM
ma-227	221	4	]	]	PUNCT
ma-227	221	5	m.	m.	NOUN
ma-227	221	6	akel	akel	PROPN
ma-227	221	7	,	,	PUNCT
ma-227	221	8	s.	s.	PROPN
ma-227	221	9	mondal	mondal	PROPN
ma-227	221	10	,	,	PUNCT
ma-227	221	11	dirichlet	dirichlet	PROPN
ma-227	221	12	problems	problem	NOUN
ma-227	221	13	in	in	ADP
ma-227	221	14	lens	lens	NOUN
ma-227	221	15	and	and	CCONJ
ma-227	221	16	lune	lune	PROPN
ma-227	221	17	,	,	PUNCT
ma-227	221	18	bull	bull	NOUN
ma-227	221	19	.	.	PUNCT
ma-227	222	1	malays	malays	PROPN
ma-227	222	2	.	.	PUNCT
ma-227	223	1	math	math	NOUN
ma-227	223	2	.	.	PUNCT
ma-227	224	1	sci	sci	PROPN
ma-227	224	2	.	.	PROPN
ma-227	224	3	soc	soc	PROPN
ma-227	224	4	.	.	PUNCT
ma-227	225	1	41	41	NUM
ma-227	225	2	(	(	PUNCT
ma-227	225	3	2018	2018	NUM
ma-227	225	4	)	)	PUNCT
ma-227	226	1	1029–1043.[2	1029–1043.[2	NUM
ma-227	226	2	]	]	PUNCT
ma-227	226	3	h.	h.	PROPN
ma-227	226	4	begehr	begehr	PROPN
ma-227	226	5	,	,	PUNCT
ma-227	226	6	t.	t.	PROPN
ma-227	226	7	vaitekhovich	vaitekhovich	PROPN
ma-227	226	8	,	,	PUNCT
ma-227	226	9	harmonic	harmonic	ADJ
ma-227	226	10	boundary	boundary	ADJ
ma-227	226	11	value	value	NOUN
ma-227	226	12	problems	problem	NOUN
ma-227	226	13	in	in	ADP
ma-227	226	14	half	half	ADJ
ma-227	226	15	disc	disc	NOUN
ma-227	226	16	and	and	CCONJ
ma-227	226	17	half	half	NOUN
ma-227	226	18	ring	ring	NOUN
ma-227	226	19	,	,	PUNCT
ma-227	226	20	funct	funct	NOUN
ma-227	226	21	.	.	PUNCT
ma-227	227	1	approx	approx	PROPN
ma-227	227	2	.	.	PUNCT
ma-227	228	1	40	40	NUM
ma-227	228	2	(	(	PUNCT
ma-227	228	3	2009)251–282.[3	2009)251–282.[3	NOUN
ma-227	228	4	]	]	X
ma-227	228	5	h.	h.	PROPN
ma-227	228	6	begehr	begehr	PROPN
ma-227	228	7	,	,	PUNCT
ma-227	228	8	t.	t.	PROPN
ma-227	228	9	vaitekhovich	vaitekhovich	PROPN
ma-227	228	10	,	,	PUNCT
ma-227	228	11	schwarz	schwarz	PROPN
ma-227	228	12	problem	problem	NOUN
ma-227	228	13	in	in	ADP
ma-227	228	14	lens	lens	NOUN
ma-227	228	15	and	and	CCONJ
ma-227	228	16	lune	lune	PROPN
ma-227	228	17	,	,	PUNCT
ma-227	228	18	complex	complex	ADJ
ma-227	228	19	var	var	NOUN
ma-227	228	20	.	.	PUNCT
ma-227	229	1	epllitic	epllitic	PROPN
ma-227	229	2	equ	equ	PROPN
ma-227	229	3	.	.	PROPN
ma-227	229	4	59	59	NUM
ma-227	229	5	(	(	PUNCT
ma-227	229	6	2014	2014	NUM
ma-227	229	7	)	)	PUNCT
ma-227	229	8	76–84.[4	76–84.[4	NUM
ma-227	229	9	]	]	X
ma-227	229	10	v.p	v.p	PROPN
ma-227	229	11	.	.	PROPN
ma-227	229	12	burskii	burskii	PROPN
ma-227	229	13	,	,	PUNCT
ma-227	229	14	e.v	e.v	PROPN
ma-227	229	15	.	.	PROPN
ma-227	229	16	lesina	lesina	PROPN
ma-227	229	17	,	,	PUNCT
ma-227	229	18	on	on	ADP
ma-227	229	19	boundary	boundary	ADJ
ma-227	229	20	value	value	NOUN
ma-227	229	21	problems	problem	NOUN
ma-227	229	22	for	for	ADP
ma-227	229	23	an	an	DET
ma-227	229	24	improperly	improperly	ADV
ma-227	229	25	elliptic	elliptic	ADJ
ma-227	229	26	equation	equation	NOUN
ma-227	229	27	in	in	ADP
ma-227	229	28	a	a	DET
ma-227	229	29	circle	circle	NOUN
ma-227	229	30	,	,	PUNCT
ma-227	229	31	comput	comput	NOUN
ma-227	229	32	.	.	PUNCT
ma-227	230	1	math.math	math.math	NOUN
ma-227	230	2	.	.	PUNCT
ma-227	231	1	phys	phy	NOUN
ma-227	231	2	.	.	PUNCT
ma-227	232	1	60	60	NUM
ma-227	232	2	(	(	PUNCT
ma-227	232	3	2020	2020	NUM
ma-227	232	4	)	)	PUNCT
ma-227	232	5	1306–1321.[5	1306–1321.[5	NUM
ma-227	232	6	]	]	PUNCT
ma-227	232	7	z.	z.	PROPN
ma-227	232	8	du	du	PROPN
ma-227	232	9	,	,	PUNCT
ma-227	232	10	y.	y.	PROPN
ma-227	232	11	wang	wang	PROPN
ma-227	232	12	,	,	PUNCT
ma-227	232	13	m.	m.	PROPN
ma-227	232	14	ku	ku	PROPN
ma-227	232	15	,	,	PUNCT
ma-227	232	16	schwarz	schwarz	PROPN
ma-227	232	17	boundary	boundary	ADJ
ma-227	232	18	value	value	NOUN
ma-227	232	19	problems	problem	NOUN
ma-227	232	20	for	for	ADP
ma-227	232	21	polyanalytic	polyanalytic	ADJ
ma-227	232	22	equation	equation	NOUN
ma-227	232	23	in	in	ADP
ma-227	232	24	a	a	DET
ma-227	232	25	sector	sector	NOUN
ma-227	232	26	ring	ring	NOUN
ma-227	232	27	,	,	PUNCT
ma-227	232	28	complex	complex	ADJ
ma-227	232	29	anal.oper	anal.oper	NOUN
ma-227	232	30	.	.	PUNCT
ma-227	233	1	theory	theory	NOUN
ma-227	233	2	,	,	PUNCT
ma-227	233	3	17	17	NUM
ma-227	233	4	(	(	PUNCT
ma-227	233	5	2023	2023	NUM
ma-227	233	6	)	)	PUNCT
ma-227	233	7	33	33	NUM
ma-227	233	8	.	.	PUNCT
ma-227	234	1	https://doi.org/10.28924/ada/ma.4.15	https://doi.org/10.28924/ada/ma.4.15	PROPN
ma-227	234	2	eur	eur	PROPN
ma-227	234	3	.	.	PUNCT
ma-227	235	1	j.	j.	PROPN
ma-227	235	2	math	math	PROPN
ma-227	235	3	.	.	PUNCT
ma-227	236	1	anal	anal	PROPN
ma-227	236	2	.	.	PUNCT
ma-227	237	1	10.28924	10.28924	NUM
ma-227	237	2	/	/	SYM
ma-227	237	3	ada	ada	PROPN
ma-227	237	4	/	/	SYM
ma-227	237	5	ma.4.15	ma.4.15	PROPN
ma-227	237	6	9	9	NUM
ma-227	238	1	[	[	SYM
ma-227	238	2	6	6	NUM
ma-227	238	3	]	]	PUNCT
ma-227	238	4	h.	h.	PROPN
ma-227	238	5	emkanpour	emkanpour	PROPN
ma-227	238	6	,	,	PUNCT
ma-227	238	7	n.	n.	PROPN
ma-227	238	8	taghizadeh	taghizadeh	PROPN
ma-227	238	9	,	,	PUNCT
ma-227	238	10	three	three	NUM
ma-227	238	11	boundary	boundary	ADJ
ma-227	238	12	value	value	NOUN
ma-227	238	13	problems	problem	NOUN
ma-227	238	14	of	of	ADP
ma-227	238	15	the	the	DET
ma-227	238	16	cauchy	cauchy	PROPN
ma-227	238	17	–	–	PUNCT
ma-227	238	18	riemann	riemann	PROPN
ma-227	238	19	equation	equation	NOUN
ma-227	238	20	in	in	ADP
ma-227	238	21	eclipse	eclipse	NOUN
ma-227	238	22	domain	domain	NOUN
ma-227	238	23	,	,	PUNCT
ma-227	238	24	complex	complex	ADJ
ma-227	238	25	var	var	NOUN
ma-227	238	26	.	.	PUNCT
ma-227	239	1	epllitic	epllitic	PROPN
ma-227	239	2	equ	equ	PROPN
ma-227	239	3	.	.	PROPN
ma-227	239	4	67	67	NUM
ma-227	239	5	(	(	PUNCT
ma-227	239	6	2022	2022	NUM
ma-227	239	7	)	)	PUNCT
ma-227	240	1	510–529.[7	510–529.[7	NUM
ma-227	240	2	]	]	X
ma-227	240	3	y.	y.	PROPN
ma-227	240	4	gao	gao	PROPN
ma-227	240	5	,	,	PUNCT
ma-227	240	6	y.	y.	PROPN
ma-227	240	7	zhao	zhao	PROPN
ma-227	240	8	,	,	PUNCT
ma-227	240	9	b.	b.	PROPN
ma-227	240	10	zhao	zhao	PROPN
ma-227	240	11	,	,	PUNCT
ma-227	240	12	boundary	boundary	ADJ
ma-227	240	13	value	value	NOUN
ma-227	240	14	problems	problem	NOUN
ma-227	240	15	of	of	ADP
ma-227	240	16	holomorphic	holomorphic	ADJ
ma-227	240	17	vector	vector	NOUN
ma-227	240	18	functions	function	NOUN
ma-227	240	19	in	in	ADP
ma-227	240	20	1d	1d	NUM
ma-227	240	21	qcs	qc	NOUN
ma-227	240	22	,	,	PUNCT
ma-227	240	23	physica	physica	PROPN
ma-227	240	24	b.	b.	PROPN
ma-227	240	25	394(2007	394(2007	NUM
ma-227	240	26	)	)	PUNCT
ma-227	240	27	56–61.[8	56–61.[8	NUM
ma-227	240	28	]	]	X
ma-227	240	29	v.v	v.v	PROPN
ma-227	240	30	.	.	PROPN
ma-227	240	31	karachik	karachik	PROPN
ma-227	240	32	,	,	PUNCT
ma-227	240	33	class	class	NOUN
ma-227	240	34	of	of	ADP
ma-227	240	35	neumann	neumann	NOUN
ma-227	240	36	-	-	PUNCT
ma-227	240	37	type	type	NOUN
ma-227	240	38	problems	problem	NOUN
ma-227	240	39	for	for	ADP
ma-227	240	40	the	the	DET
ma-227	240	41	polyharmonic	polyharmonic	ADJ
ma-227	240	42	equation	equation	NOUN
ma-227	240	43	in	in	ADP
ma-227	240	44	a	a	DET
ma-227	240	45	ball	ball	NOUN
ma-227	240	46	,	,	PUNCT
ma-227	240	47	comput	comput	NOUN
ma-227	240	48	.	.	PUNCT
ma-227	241	1	math	math	NOUN
ma-227	241	2	.	.	PUNCT
ma-227	242	1	math	math	NOUN
ma-227	242	2	.	.	PUNCT
ma-227	243	1	phys.60	phys.60	NUM
ma-227	243	2	(	(	PUNCT
ma-227	243	3	2020	2020	NUM
ma-227	243	4	)	)	PUNCT
ma-227	243	5	144–162.[9	144–162.[9	NUM
ma-227	243	6	]	]	X
ma-227	243	7	v.g	v.g	PROPN
ma-227	243	8	.	.	PROPN
ma-227	243	9	nikolaev	nikolaev	PROPN
ma-227	243	10	,	,	PUNCT
ma-227	243	11	schwarz	schwarz	PROPN
ma-227	243	12	problem	problem	NOUN
ma-227	243	13	for	for	ADP
ma-227	243	14	j	j	PROPN
ma-227	243	15	-	-	PUNCT
ma-227	243	16	analytic	analytic	ADJ
ma-227	243	17	functions	function	NOUN
ma-227	243	18	in	in	ADP
ma-227	243	19	an	an	DET
ma-227	243	20	ellipse	ellipse	NOUN
ma-227	243	21	,	,	PUNCT
ma-227	243	22	comput	comput	NOUN
ma-227	243	23	.	.	PUNCT
ma-227	244	1	math	math	NOUN
ma-227	244	2	.	.	PUNCT
ma-227	245	1	math	math	NOUN
ma-227	245	2	.	.	PUNCT
ma-227	246	1	phys	phy	NOUN
ma-227	246	2	.	.	PUNCT
ma-227	247	1	62	62	NUM
ma-227	247	2	(	(	PUNCT
ma-227	247	3	2022	2022	NUM
ma-227	247	4	)	)	PUNCT
ma-227	247	5	1089–1111.[10	1089–1111.[10	NUM
ma-227	247	6	]	]	X
ma-227	247	7	a.v	a.v	PROPN
ma-227	247	8	.	.	PROPN
ma-227	247	9	petukhov	petukhov	PROPN
ma-227	247	10	,	,	PUNCT
ma-227	247	11	a.o	a.o	PROPN
ma-227	247	12	.	.	PROPN
ma-227	247	13	savchenko	savchenko	PROPN
ma-227	247	14	,	,	PUNCT
ma-227	247	15	solution	solution	NOUN
ma-227	247	16	of	of	ADP
ma-227	247	17	the	the	DET
ma-227	247	18	exterior	exterior	ADJ
ma-227	247	19	boundary	boundary	ADJ
ma-227	247	20	value	value	NOUN
ma-227	247	21	problem	problem	NOUN
ma-227	247	22	for	for	ADP
ma-227	247	23	the	the	DET
ma-227	247	24	helmholtz	helmholtz	NOUN
ma-227	247	25	equation	equation	NOUN
ma-227	247	26	usingoverlapping	usingoverlappe	VERB
ma-227	247	27	domain	domain	NOUN
ma-227	247	28	decomposition	decomposition	NOUN
ma-227	247	29	,	,	PUNCT
ma-227	247	30	comput	comput	NOUN
ma-227	247	31	.	.	PUNCT
ma-227	248	1	math	math	NOUN
ma-227	248	2	.	.	PUNCT
ma-227	249	1	math	math	NOUN
ma-227	249	2	.	.	PUNCT
ma-227	250	1	phys	phy	NOUN
ma-227	250	2	.	.	PUNCT
ma-227	251	1	62	62	NUM
ma-227	251	2	(	(	PUNCT
ma-227	251	3	2020	2020	NUM
ma-227	251	4	)	)	PUNCT
ma-227	252	1	784–796.[11	784–796.[11	PROPN
ma-227	252	2	]	]	PUNCT
ma-227	252	3	k.	k.	PROPN
ma-227	252	4	ravikumar	ravikumar	PROPN
ma-227	252	5	,	,	PUNCT
ma-227	252	6	k.	k.	PROPN
ma-227	252	7	ramkumar	ramkumar	PROPN
ma-227	252	8	,	,	PUNCT
ma-227	252	9	d.	d.	PROPN
ma-227	252	10	chalishajar	chalishajar	PROPN
ma-227	252	11	,	,	PUNCT
ma-227	252	12	existence	existence	NOUN
ma-227	252	13	and	and	CCONJ
ma-227	252	14	stability	stability	NOUN
ma-227	252	15	results	result	NOUN
ma-227	252	16	for	for	ADP
ma-227	252	17	second	second	ADJ
ma-227	252	18	-	-	PUNCT
ma-227	252	19	order	order	NOUN
ma-227	252	20	neutral	neutral	ADJ
ma-227	252	21	stochasticdifferential	stochasticdifferential	ADJ
ma-227	252	22	equations	equation	NOUN
ma-227	252	23	with	with	ADP
ma-227	252	24	random	random	ADJ
ma-227	252	25	impulses	impulse	NOUN
ma-227	252	26	and	and	CCONJ
ma-227	252	27	poisson	poisson	NOUN
ma-227	252	28	jumps	jump	VERB
ma-227	252	29	,	,	PUNCT
ma-227	252	30	eur	eur	PROPN
ma-227	252	31	.	.	PUNCT
ma-227	253	1	j.	j.	PROPN
ma-227	253	2	math	math	PROPN
ma-227	253	3	.	.	PUNCT
ma-227	254	1	anal	anal	ADJ
ma-227	254	2	.	.	PUNCT
ma-227	255	1	1	1	NUM
ma-227	255	2	(	(	PUNCT
ma-227	255	3	2021	2021	NUM
ma-227	255	4	)	)	PUNCT
ma-227	256	1	1.[12	1.[12	NUM
ma-227	256	2	]	]	X
ma-227	256	3	n.	n.	PROPN
ma-227	256	4	taghizadeh	taghizadeh	PROPN
ma-227	256	5	,	,	PUNCT
ma-227	256	6	m.	m.	NOUN
ma-227	256	7	mirzazadeh	mirzazadeh	PROPN
ma-227	256	8	,	,	PUNCT
ma-227	256	9	f.	f.	PROPN
ma-227	256	10	farahrooz	farahrooz	PROPN
ma-227	256	11	,	,	PUNCT
ma-227	256	12	exact	exact	ADJ
ma-227	256	13	solutions	solution	NOUN
ma-227	256	14	of	of	ADP
ma-227	256	15	the	the	DET
ma-227	256	16	nonlinear	nonlinear	ADJ
ma-227	256	17	schrödinger	schrödinger	ADJ
ma-227	256	18	equation	equation	NOUN
ma-227	256	19	by	by	ADP
ma-227	256	20	the	the	DET
ma-227	256	21	firstintegral	firstintegral	ADJ
ma-227	256	22	method	method	NOUN
ma-227	256	23	,	,	PUNCT
ma-227	256	24	j.	j.	PROPN
ma-227	256	25	math	math	PROPN
ma-227	256	26	.	.	PUNCT
ma-227	257	1	anal	anal	PROPN
ma-227	257	2	.	.	PUNCT
ma-227	258	1	appl	appl	PROPN
ma-227	258	2	.	.	PUNCT
ma-227	259	1	374	374	NUM
ma-227	259	2	(	(	PUNCT
ma-227	259	3	2011	2011	NUM
ma-227	259	4	)	)	PUNCT
ma-227	259	5	549–553.[13	549–553.[13	PROPN
ma-227	259	6	]	]	PUNCT
ma-227	259	7	n.	n.	PROPN
ma-227	259	8	taghizadeh	taghizadeh	PROPN
ma-227	259	9	,	,	PUNCT
ma-227	259	10	v.s.	v.s.	ADJ
ma-227	259	11	mohammadi	mohammadi	NOUN
ma-227	259	12	,	,	PUNCT
ma-227	259	13	some	some	DET
ma-227	259	14	boundary	boundary	ADJ
ma-227	259	15	value	value	NOUN
ma-227	259	16	problems	problem	NOUN
ma-227	259	17	for	for	ADP
ma-227	259	18	the	the	DET
ma-227	259	19	cauchy	cauchy	PROPN
ma-227	259	20	–	–	PUNCT
ma-227	259	21	riemann	riemann	PROPN
ma-227	259	22	equation	equation	NOUN
ma-227	259	23	in	in	ADP
ma-227	259	24	half	half	ADJ
ma-227	259	25	lens	len	NOUN
ma-227	259	26	,	,	PUNCT
ma-227	259	27	eurasian	eurasian	PROPN
ma-227	259	28	math	math	NOUN
ma-227	259	29	j.	j.	PROPN
ma-227	259	30	9	9	NUM
ma-227	259	31	(	(	PUNCT
ma-227	259	32	2018	2018	NUM
ma-227	259	33	)	)	PUNCT
ma-227	259	34	73–84.[14	73–84.[14	NUM
ma-227	259	35	]	]	X
ma-227	259	36	i.n	i.n	PROPN
ma-227	259	37	.	.	PROPN
ma-227	259	38	vekua	vekua	NOUN
ma-227	259	39	,	,	PUNCT
ma-227	259	40	generalized	generalized	ADJ
ma-227	259	41	analytic	analytic	ADJ
ma-227	259	42	functions	function	NOUN
ma-227	259	43	,	,	PUNCT
ma-227	259	44	pergamon	pergamon	PROPN
ma-227	259	45	press	press	PROPN
ma-227	259	46	,	,	PUNCT
ma-227	259	47	oxford	oxford	PROPN
ma-227	259	48	,	,	PUNCT
ma-227	259	49	1962.[15	1962.[15	PROPN
ma-227	259	50	]	]	X
ma-227	259	51	y.	y.	PROPN
ma-227	259	52	wang	wang	PROPN
ma-227	259	53	,	,	PUNCT
ma-227	259	54	x.	x.	PROPN
ma-227	259	55	zhao	zhao	PROPN
ma-227	259	56	,	,	PUNCT
ma-227	259	57	schwarz	schwarz	PROPN
ma-227	259	58	boundary	boundary	ADJ
ma-227	259	59	value	value	NOUN
ma-227	259	60	problem	problem	NOUN
ma-227	259	61	for	for	ADP
ma-227	259	62	the	the	DET
ma-227	259	63	cauchy	cauchy	PROPN
ma-227	259	64	–	–	PUNCT
ma-227	259	65	riemann	riemann	PROPN
ma-227	259	66	equation	equation	NOUN
ma-227	259	67	in	in	ADP
ma-227	259	68	a	a	DET
ma-227	259	69	rectangle	rectangle	NOUN
ma-227	259	70	,	,	PUNCT
ma-227	259	71	bound	bind	VERB
ma-227	259	72	.	.	PUNCT
ma-227	260	1	valueprobl	valueprobl	PROPN
ma-227	260	2	.	.	PUNCT
ma-227	261	1	2016	2016	NUM
ma-227	261	2	(	(	PUNCT
ma-227	261	3	2016	2016	NUM
ma-227	261	4	)	)	PUNCT
ma-227	262	1	7.[16	7.[16	NUM
ma-227	262	2	]	]	X
ma-227	262	3	y.	y.	PROPN
ma-227	262	4	wang	wang	PROPN
ma-227	262	5	,	,	PUNCT
ma-227	262	6	schwarz	schwarz	NOUN
ma-227	262	7	-	-	PUNCT
ma-227	262	8	type	type	NOUN
ma-227	262	9	boundary	boundary	ADJ
ma-227	262	10	value	value	NOUN
ma-227	262	11	problems	problem	NOUN
ma-227	262	12	for	for	ADP
ma-227	262	13	the	the	DET
ma-227	262	14	polyanalytic	polyanalytic	ADJ
ma-227	262	15	equation	equation	NOUN
ma-227	262	16	in	in	ADP
ma-227	262	17	the	the	DET
ma-227	262	18	half	half	ADJ
ma-227	262	19	unit	unit	NOUN
ma-227	262	20	disc	disc	NOUN
ma-227	262	21	,	,	PUNCT
ma-227	262	22	complex	complex	ADJ
ma-227	262	23	var.epllitic	var.epllitic	ADJ
ma-227	262	24	equ	equ	PROPN
ma-227	262	25	.	.	PROPN
ma-227	262	26	57	57	NUM
ma-227	262	27	(	(	PUNCT
ma-227	262	28	2012	2012	NUM
ma-227	262	29	)	)	PUNCT
ma-227	262	30	983–993	983–993	NUM
ma-227	262	31	.	.	PUNCT
ma-227	263	1	https://doi.org/10.28924/ada/ma.4.15	https://doi.org/10.28924/ada/ma.4.15	PROPN
ma-227	263	2	1	1	NUM
ma-227	263	3	.	.	PUNCT
ma-227	263	4	introduction	introduction	NOUN
ma-227	263	5	and	and	CCONJ
ma-227	263	6	preliminaries	preliminary	NOUN
ma-227	263	7	2	2	NUM
ma-227	263	8	.	.	PUNCT
ma-227	264	1	an	an	DET
ma-227	264	2	integral	integral	ADJ
ma-227	264	3	representation	representation	NOUN
ma-227	264	4	formula	formula	NOUN
ma-227	264	5	for	for	ADP
ma-227	264	6	m	m	PROPN
ma-227	264	7	3	3	NUM
ma-227	264	8	.	.	PUNCT
ma-227	265	1	dirichlet	dirichlet	PROPN
ma-227	265	2	problem	problem	NOUN
ma-227	265	3	for	for	ADP
ma-227	265	4	the	the	DET
ma-227	265	5	cauchy	cauchy	PROPN
ma-227	265	6	–	–	PUNCT
ma-227	265	7	riemann	riemann	PROPN
ma-227	265	8	equation	equation	NOUN
ma-227	265	9	in	in	ADP
ma-227	265	10	m	m	NOUN
ma-227	265	11	acknowledgments	acknowledgment	NOUN
ma-227	265	12	declarations	declaration	NOUN
ma-227	265	13	references	reference	NOUN