Integral representation of solutions to Fuchsian system and Heun's equation

Abstract

We obtain integral representations of solutions to special cases of the Fuchsian system of differential equations and Heun's differential equation. In particular, we calculate the monodromy of solutions to the Fuchsian equation that corresponds to Picard's solution of the sixth Painlev\'e equation, and to Heun's equation.Comment: 21 page