
eBook ISBN: | 978-1-4704-4056-5 |
Product Code: | MEMO/248/1177.E |
List Price: | $75.00 |
MAA Member Price: | $67.50 |
AMS Member Price: | $45.00 |

eBook ISBN: | 978-1-4704-4056-5 |
Product Code: | MEMO/248/1177.E |
List Price: | $75.00 |
MAA Member Price: | $67.50 |
AMS Member Price: | $45.00 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 248; 2017; 96 ppMSC: Primary 33; Secondary 13
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.
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Table of Contents
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Chapters
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1. Introduction
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2. Preliminaries
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3. Derivation of special values
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4. Tables of special values
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A. Some hypergeometric identities for generalized hypergeometric series and Appell-Lauricella hypergeometric series
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Acknowledgments
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Additional Material
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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.
-
Chapters
-
1. Introduction
-
2. Preliminaries
-
3. Derivation of special values
-
4. Tables of special values
-
A. Some hypergeometric identities for generalized hypergeometric series and Appell-Lauricella hypergeometric series
-
Acknowledgments