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Equi-Distribution of Values for the Third and the Fifth Painlevé Transcendents

Published online by Cambridge University Press:  11 January 2016

Shun Shimomura
Shun Shimomura*
Affiliation:
Department of Mathematics Keio University, 3-14-1, Hiyoshi, Kohoku-ku Yokohama 223-8522, Japan, shimomur@math.keio.ac.jp
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Abstract

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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.

Keywords

34M5534M0530D35
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 192 , 2008 , pp. 89 - 109
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2008

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