Functional Equations for Appell's F1 Arising from Transformations of Elliptic Curves

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概要

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• We give a functional equation for Appell's hypergeometric function F1, which arises from transformations of elliptic curves. As an application, we give an efficient algorithm for computing incomplete elliptic integrals of the first kind. We also give a reduction formula that simplifies Lauricella's hypergeometric function FD of five variables to F1.

• 日本数学会函数方程式論分科会の論文

著者

• Goto Yoshiaki

  Hokkaido University

関連論文

• Functional Equations for Appell's F1 Arising from Transformations of Elliptic Curves

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