10E9 solution to the elliptic Painlevé equation

Kenji Kajiwara, Tetsu Masuda, Masatoshi Noumi, Yasuhiro Ohta, Yasuhiko Yamada

Research output: Contribution to journalArticlepeer-review

50 Citations (Scopus)


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 10E9.

Original languageEnglish
Pages (from-to)L263-L272
JournalJournal of Physics A: Mathematical and General
Issue number17
Publication statusPublished - May 2 2003

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • General Physics and Astronomy


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