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Heun equation and Painlevé equation

Kouichi Takemura
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Abstract

We relate two parameter solutions of the sixth Painlevé equation and finite-gap solutions of the Heun equation by considering monodromy on a certain class of Fuchsian differential equations. In the appendix, we present formulae on differentials of elliptic modular functions, and obtain the ellitic form of the sixth Painlevé equation directly.

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Kouichi Takemura. 2005-03-15. Heun equation and Painlevé equation. https://arxiv.org/abs/math/0503288

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