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arXiv · 1809.02311

A Riemann-Hilbert Approach to the Heun Equation

Boris Dubrovin·Andrei Kapaev
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Abstract

We describe the close connection between the linear system for the sixth Painlev\'e equation and the general Heun equation, formulate the Riemann-Hilbert problem for the Heun functions and show how, in the case of reducible monodromy, the Riemann-Hilbert formalism can be used to construct explicit polynomial solutions of the Heun equation.

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BibTeXRIS

Boris Dubrovin, Andrei Kapaev. 2018-09-07. A Riemann-Hilbert Approach to the Heun Equation. https://doi.org/10.3842/sigma.2018.093

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