Special values of Gauss's hypergeometric series derived from Appell's series F₁ with closed forms

2016/07/16 by Akihito Ebisu, Ebisu, Akihito
Mathematics · #Advanced Mathematical Identities #History and Theory of Mathematics #Mathematics and Applications #math.CA #msc:13P15 #msc:33C05 #msc:33C65 #msc:33F10

paper · pdf · doi:10.48550/arxiv.1607.04742

16 pages, 5 tables, 1 figure

arxiv created 2016/07/19 · arxiv updated 2016/07/20

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 ₂F₁ possessing closed forms. Here, we consider the application of this method to Appell's hypergeometetric series F₁ and derive several F₁ possessing closed forms. Moreover, analyzing these F₁, we obtain values of ₂F₁ with no free parameters. Some of these results provide new examples of algebraic values of ₂F₁. Key Words and Phrases: Gauss's hypergeometric series, algebraic value, Appell's hypergeometric series, hypergeometric identity.

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