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arXiv · 0807.0258

An Isomonodromy Interpretation of the Hypergeometric Solution of the Elliptic Painlev\'e Equation (and Generalizations)

Eric M. Rains
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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.

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Eric M. Rains. 2008-07-02. An Isomonodromy Interpretation of the Hypergeometric Solution of the Elliptic Painlev\'e Equation (and Generalizations). https://doi.org/10.3842/sigma.2011.088

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