Integral representation of solutions to Fuchsian system and Heun's equation
arXiv:0705.3358 · doi:10.1016/j.jmaa.2007.11.015
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 Painlevé equation, and to Heun's equation.
21 pages
References in corpus (8)
- The Heun equation and the Calogero-Moser-Sutherland system I: the Bethe Ansatz method
- The Heun equation and the Calogero-Moser-Sutherland system II: perturbation and algebraic solution
- The Heun equation and the Calogero-Moser-Sutherland system IV: the Hermite-Krichever Ansatz
- On the middle convolution
- The Heun equation and the Calogero-Moser-Sutherland system V: generalized Darboux transformations
- Heun equation and Painlevé equation
- Finite-gap potential, Heun's differential equation and WKB analysis
- Fuchsian equation, Hermite-Krichever Ansatz and Painlevé equation
Cited by in corpus (5)
- Expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta and the Appell generalized hypergeometric functions
- Middle Convolution and Heun's Equation
- Integral transformation of Heun's equation and some applications
- Symmetries of quantum Lax equations for the Painlevé equations
- -Middle Convolution and -Painlevé Equation