Heun equation and Painlev\'e equation
Classical Analysis and ODEs
2007-05-23 v1 Mathematical Physics
math.MP
Quantum Algebra
Exactly Solvable and Integrable Systems
Abstract
We relate two parameter solutions of the sixth Painlev\'e 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 Painlev\'e equation directly.
Cite
@article{arxiv.math/0503288,
title = {Heun equation and Painlev\'e equation},
author = {Kouichi Takemura},
journal= {arXiv preprint arXiv:math/0503288},
year = {2007}
}
Comments
17 pages, based on the talk given at the Workshop "Studies on elliptic integrable systems" (Kyoto, November 2004)