Functional Equations for Appell's <i>F</i><sub>1</sub> Arising from Transformations of Elliptic Curves

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Author(s)

Abstract

We give a functional equation for Appell's hypergeometric function <i>F</i><sub>1</sub>, 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 <i>F</i><sub><i>D</i></sub> of five variables to <i>F</i><sub>1</sub>.

Journal

  • Funkcialaj Ekvacioj

    Funkcialaj Ekvacioj 56(3), 379-396, 2013

    Division of Functional Equations, The Mathematical Society of Japan

Codes

  • NII Article ID (NAID)
    130003382751
  • Text Lang
    ENG
  • ISSN
    0532-8721
  • Data Source
    J-STAGE 
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