3 papers
math.CA2005★ 6 cited
Heun equation and Painlevé equation
Kouichi Takemura
We relate two parameter solutions of the sixth Painlevé equation and finite-gap solutions of the Heun equation by considering monodromy on a certain class of Fuchsian differential…
math.CA2005★ 2 cited
Fuchsian equation, Hermite-Krichever Ansatz and Painlevé equation
Kouichi Takemura
Several results on Heun's equation are generalized to a certain class of Fuchsian differential equations. Namely, we obtain integral representations of solutions and develop Hermit…
math.CA2004★ 4 cited
On eigenvalues of Lamé operator
Kouichi Takemura
We introduce two integral representations of monodromy on Lamé equation. By applying them, we obtain results on hyperelliptic-to-elliptic reduction integral formulae, finite-gap po…