Padé interpolation for elliptic Painlevé equation

Abstract

An interpolation problem related to the elliptic Painlevé equation is formulated and solved. A simple form of the elliptic Painlevé equation and the Lax pair are obtained. Explicit determinant formulae of special solutions are also given.

17 pages. Dedicated to Professor Michio Jimbo on his 60th birthday. To appear in the proceedings of the international workshop "Infinite Analysis 11"

References in corpus (3)

• Essays on the theory of elliptic hypergeometric functions
• Hypergeometric solutions to the q-Painlevé equations
• New Expressions for Discrete Painlevé Equations

Cited by in corpus (5)

• An Elliptic Garnier System from Interpolation
• Quadrirational Yang-Baxter maps and the affine-E8 Painleve lattice
• An elliptic Garnier system
• Direct Connection between the R_{II} Chain and the Nonautonomous Discrete Modified KdV Lattice
• A Variation of the $q$-Painlevé System with Affine Weyl Group Symmetry of Type $E_7^{(1)}$