Title: Special Values of the Hypergeometric Series
Abstract: In this paper, we present 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, we get identities for the hypergeometric series F(a,b;c;x); we show 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. We tabulate the values of F(a,b;c;x) that can be obtained with this method. We find that this set includes almost all previously known values and many previously unknown values.
Publication Year: 2017
Publication Date: 2017-06-25
Language: en
Type: book
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Cited By Count: 12
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