Special Values of the Hypergeometric Series

Ebook Details


Akihito Ebisu

Year 2017
Pages 96
Publisher Amer Mathematical Society
Language en
ISBN 9781470425333
File Size 560.33 KB
File Format PDF
Download Counter 101
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Ebook Description

In this paper, the author presents a new method for finding identities for hypergeoemtric series, such as the (Gauss) hypergeometric series, the generalized hypergeometric series and the Appell-Lauricella hypergeometric series. Furthermore, using this method, the author gets identities for the hypergeometric series $F(a,b;c;x)$ and shows that values of $F(a,b;c;x)$ at some points $x$ can be expressed in terms of gamma functions, together with certain elementary functions. The author tabulates the values of $F(a,b;c;x)$ that can be obtained with this method and finds that this set includes almost all previously known values and many previously unknown values.