Abstract
A τ function formalism for Sakai's elliptic Painleve 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 Painleve 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 Painleve equation expressed in terms of the elliptic hypergeometric function 10E9.
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