10E9 solution to the elliptic Painlevé equation

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

Research output: Contribution to journalArticle

46 Citations (Scopus)

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 10E9.

Original languageEnglish
Pages (from-to)L263-L272
JournalJournal of Physics A: Mathematical and General
Volume36
Issue number17
DOIs
Publication statusPublished - May 2 2003

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Elliptic Equations
Addition formula
formulations
hypergeometric functions
elliptic functions
Formulation
Elliptic function
Particular Solution
Hypergeometric Functions
Elliptic Curves
equivalence
Die
Equivalence
formalism
curves

All Science Journal Classification (ASJC) codes

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

Cite this

10E9 solution to the elliptic Painlevé equation. / Kajiwara, Kenji; Masuda, Tetsu; Noumi, Masatoshi; Ohta, Yasuhiro; Yamada, Yasuhiko.

In: Journal of Physics A: Mathematical and General, Vol. 36, No. 17, 02.05.2003, p. L263-L272.

Research output: Contribution to journalArticle

Kajiwara, Kenji ; Masuda, Tetsu ; Noumi, Masatoshi ; Ohta, Yasuhiro ; Yamada, Yasuhiko. / 10E9 solution to the elliptic Painlevé equation. In: Journal of Physics A: Mathematical and General. 2003 ; Vol. 36, No. 17. pp. L263-L272.
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