MR3157148
Yoshiaki GOTO
Yoshiaki GOTO
Functional Equations for Appell's $F_1$ Arising from Transformations of Elliptic Curves
Funkcialaj Ekvacioj. Serio Internacia
56
2013
379--396
http://fe.math.kobe-u.ac.jp/FE/FullPapers/56-3/56_379.pdf
http://www.ams.org/mathscinet-getitem?mr=MR3157148
We give a functional equation for Appell's hypergeometric function $F_1$, which arises from transformations of elliptic curves. As an application, we give an efficient algorithm computing incomplete elliptic integrals of the first kind. We also give a reduction formula from Lauricella's hypergeometric function $F_D$ of five variables to $F_1$.
Hypergeometric Functions, Transformation Formulas, Incomplete Elliptic Integrals of the First Kind.
33C65, 33C75.
56-379
2013
Functional Equations for Appell's $F_1$ Arising from Transformations of Elliptic Curves
Yoshiaki GOTO
Yoshiaki GOTO
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