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Zbl 1052.34085
Masuda, Tetsu; Ohta, Yasuhiro; Kajiwara, Kenji
A determinant formula for a class of rational solutions of Painlevé V equation. (English)
[J] Nagoya Math. J. 168, 1-25 (2002). ISSN 0027-7630

The authors give general forms of a certain class of rational solutions of the fifth Painlevé equation $P_5$ with exploiting universal characters introduced by Koike. The class which they are considering here is that of the rational solutions of $P_5$ not appearing on any wall of the parameter space of $P_5$ with respect to the $A_3$-Weyl-group action. This work is considered as a continuation of a series of previous works in which the same authors gave analogous formulas of rational solutions of the second, third and fourth Painlevé equations. The main result in this paper is a generalization of the result obtained by Noumi and Yamada in a special case of the parameters of $P_5$.
[Humihiko Watanabe (Hokkaido)]

MSC 2000:: *34M55 Painlevé and other special equations
33E17 Painlevé-type functions

Keywords: rational solution; universal character; Umemura polynomial; Painlevé equation

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