An Isomonodromy Interpretation of the Hypergeometric Solution of the Elliptic Painlevé Equation (and Generalizations)

Symmetry Integrability and Geometry-Methods and Applications

article

Eric M. Rains¹ 

[1] Department of Mathematics, California Institute of Technology

关键词: isomonodromy;    hypergeometric;    Painlev´e;    biorthogonal functions;   

DOI  :  10.3842/SIGMA.2011.088

来源: National Academy of Science of Ukraine

【 摘 要 】

We construct a family of second-order linear difference equations parametrized by the hypergeometric solution of the elliptic Painlevé equation (or higher-order analogues), and admitting a large family of monodromy-preserving deformations. The solutions are certain semiclassical biorthogonal functions (and their Cauchy transforms), biorthogonal with respect to higher-order analogues of Spiridonov's elliptic beta integral.

【 授权许可】

Unknown