Heun equation and Painlevé equation

Details Heun equation and Painlevé equation Heun equation and Painlevé equation

2005-03-15

arxiv.org/abs/math/0503288v1

Mathematics

Classical Analysis and ODEs

17 pages, based on the talk given at the Workshop "Studies on elliptic integrable systems" (Kyoto, November 2004)

Scientific paper

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.

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