Special values of the hypergeometric series
著者
書誌事項
Special values of the hypergeometric series
（Memoirs of the American Mathematical Society, no. 1177）
American Mathematical Society, 2017
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注記
"Volume 248, number 1177 (third of 5 numbers), July 2017"
Bibliography: p. 95-96
内容説明・目次
内容説明
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.
目次
Introduction
Preliminaries
Derivation of special values
Tables of special values
Appendix A. Some hypergeometric identities for generalized hypergeometric series and Appell-Lauricella hypergeometric series
Acknowledgments
Bibliography.
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