Middle Convolution and Heun's Equation
Classical Analysis and ODEs
2009-04-03 v3 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Abstract
Heun's equation naturally appears as special cases of Fuchsian system of differential equations of rank two with four singularities by introducing the space of initial conditions of the sixth Painlev\'e equation. Middle convolutions of the Fuchsian system are related with an integral transformation of Heun's equation.
Cite
@article{arxiv.0810.3112,
title = {Middle Convolution and Heun's Equation},
author = {Kouichi Takemura},
journal= {arXiv preprint arXiv:0810.3112},
year = {2009}
}