### Abstract

A τ function formalism for Sakai's elliptic Painlevé 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 Painlevé equation as a non-autonomous deformation of the addition formula on elliptic curves. By using these formulations, we construct a particular solution of die elliptic Painlevé equation expressed in terms of the elliptic hypergeometric function _{10}E_{9}.

Original language | English |
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Pages (from-to) | L263-L272 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 36 |

Issue number | 17 |

DOIs | |

Publication status | Published - May 2 2003 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)

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## Cite this

Kajiwara, K., Masuda, T., Noumi, M., Ohta, Y., & Yamada, Y. (2003). 10E9 solution to the elliptic Painlevé equation.

*Journal of Physics A: Mathematical and General*,*36*(17), L263-L272. https://doi.org/10.1088/0305-4470/36/17/102