A Riemann-Hilbert Approach to the Heun Equation
Classical Analysis and ODEs
2018-09-10 v1 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
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.
Keywords
Cite
@article{arxiv.1809.02311,
title = {A Riemann-Hilbert Approach to the Heun Equation},
author = {Boris Dubrovin and Andrei Kapaev},
journal= {arXiv preprint arXiv:1809.02311},
year = {2018}
}