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On the Umemura polynomials for the Painlevé III equation

✍ Scribed by Kenji Kajiwara; Tetsu Masuda

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
66 KB
Volume
260
Category
Article
ISSN
0375-9601

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✦ Synopsis

A determinant expression of Jacobi-Trudi type for the rational solutions of the Painleve III P equation is presented.

´III

Entries of determinant are given by the Laguerre polynomials. Degeneration of this determinant expression to that for the rational solutions of P is discussed by applying the coalescence procedure.

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Quadratic transformations for the sixth
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A new type of transformation is found for the Painlev6 six equation which can be considered as an analog of the well-known quadratic transformations for hypergeometric functions.