_10E_9 solution to the elliptic Painlev'e equation

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A $τ$ function formalism for Sakai's elliptic Painlev'e equation is presented. This establishes the equivalence between the two formulations by Sakai and by Ohta-Ramani-Grammaticos. We also give a simple geometric description of the elliptic Painlev'e equation as a non-autonomous deformation of the addition formula on elliptic curves. By using these formulations, we construct a particular solution of the elliptic Painlev'e equation expressed in terms of the elliptic hypergeometric function_10E_9.
12 pages

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Exactly Solvable and Integrable Systems, Quantum Algebra

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http://salesiana.dossiersoluciones.com/handle/123456789/80433

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/nlin/0303032
 http://arxiv.org/abs/nlin/0303032

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arXiv