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arXiv · 1607.04742

Special values of Gauss's hypergeometric series derived from Appell's series $F_1$ with closed forms

Akihito Ebisu
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Abstract

In a previous work ([Eb]), the author proposed a method employing contiguity relations to derive hypergeometric series in closed form. In [Eb], this method was used to derive Gauss's hypergeometric series $_2F_1$ possessing closed forms. Here, we consider the application of this method to Appell's hypergeometetric series $F_1$ and derive several $F_1$ possessing closed forms. Moreover, analyzing these $F_1$, we obtain values of $_2F_1$ with no free parameters. Some of these results provide new examples of algebraic values of $_2F_1$. Key Words and Phrases: Gauss's hypergeometric series, algebraic value, Appell's hypergeometric series, hypergeometric identity.

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Akihito Ebisu. 2016-07-16. Special values of Gauss's hypergeometric series derived from Appell's series $F_1$ with closed forms. https://arxiv.org/abs/1607.04742

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