An Isomonodromy Interpretation of the Hypergeometric Solution of the Elliptic Painlev\'e Equation (and Generalizations)
Classical Analysis and ODEs
2011-09-12 v2 Exactly Solvable and Integrable Systems
Abstract
We construct a family of second-order linear difference equations parametrized by the hypergeometric solution of the elliptic Painlev\'e 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.
Keywords
Cite
@article{arxiv.0807.0258,
title = {An Isomonodromy Interpretation of the Hypergeometric Solution of the Elliptic Painlev\'e Equation (and Generalizations)},
author = {Eric M. Rains},
journal= {arXiv preprint arXiv:0807.0258},
year = {2011}
}