Equi-distribution of values for the third and the fifth Painlevé transcendents

Shun Shimomura

doi:10.1017/s0027763000025988

Equi-distribution of values for the third and the fifth Painlevé transcendents

Shun Shimomura

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We show equi-distribution properties of values for the third and the fifth Painlevé transcendents in a sectorial domain. For our purpose we define a characteristic function of sectorial domain type by employing value distribution theory in a half plane. Some special cases admit analogues of Borel exceptional values. Similar results are obtained for modified versions of these Painlevé transcendents, which are of infinite growth order.

Original language	English
Pages (from-to)	89-109
Number of pages	21
Journal	Nagoya Mathematical Journal
Volume	192
DOIs	https://doi.org/10.1017/s0027763000025988
Publication status	Published - 2008
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)

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10.1017/s0027763000025988

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title = "Equi-distribution of values for the third and the fifth Painlev{\'e} transcendents",

abstract = "We show equi-distribution properties of values for the third and the fifth Painlev{\'e} transcendents in a sectorial domain. For our purpose we define a characteristic function of sectorial domain type by employing value distribution theory in a half plane. Some special cases admit analogues of Borel exceptional values. Similar results are obtained for modified versions of these Painlev{\'e} transcendents, which are of infinite growth order.",

author = "Shun Shimomura",

year = "2008",

doi = "10.1017/s0027763000025988",

language = "English",

volume = "192",

pages = "89--109",

journal = "Nagoya Mathematical Journal",

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AU - Shimomura, Shun

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N2 - We show equi-distribution properties of values for the third and the fifth Painlevé transcendents in a sectorial domain. For our purpose we define a characteristic function of sectorial domain type by employing value distribution theory in a half plane. Some special cases admit analogues of Borel exceptional values. Similar results are obtained for modified versions of these Painlevé transcendents, which are of infinite growth order.

AB - We show equi-distribution properties of values for the third and the fifth Painlevé transcendents in a sectorial domain. For our purpose we define a characteristic function of sectorial domain type by employing value distribution theory in a half plane. Some special cases admit analogues of Borel exceptional values. Similar results are obtained for modified versions of these Painlevé transcendents, which are of infinite growth order.

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U2 - 10.1017/s0027763000025988

DO - 10.1017/s0027763000025988

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AN - SCOPUS:67449156332

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VL - 192

SP - 89

EP - 109

JO - Nagoya Mathematical Journal

JF - Nagoya Mathematical Journal

ER -

Equi-distribution of values for the third and the fifth Painlevé transcendents

Abstract

ASJC Scopus subject areas

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