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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

No coin nor oath required. For personal study only.

✦ 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
✍ A. V. Kitaev 📂 Article 📅 1991 🏛 Springer 🌐 English ⚖ 234 KB

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.