Integral representation of solutions to Fuchsian system and Heun's equation
Kouichi Takemura
TL;DR
This paper derives integral representations for solutions to specific Fuchsian systems and Heun's equation, including monodromy calculations for special cases related to Painlevé and Heun's equations.
Contribution
It provides new integral formulas for solutions and computes monodromy for particular Fuchsian systems and Heun's equation, advancing understanding of their analytical properties.
Findings
Integral representations for solutions to special Fuchsian systems and Heun's equation.
Monodromy calculations for solutions related to Painlevé VI and Heun's equations.
Enhanced understanding of the analytical structure of these differential equations.
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.
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