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Special Values of the Hypergeometric Series
 
Akihito Ebisu Hokkaido University, Sapporo, Japan
Special Values of the Hypergeometric Series
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
Special Values of the Hypergeometric Series
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Special Values of the Hypergeometric Series
Akihito Ebisu Hokkaido University, Sapporo, Japan
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
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2482017; 96 pp
    MSC: 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.

  • Table of Contents
     
     
    • 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
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2482017; 96 pp
MSC: 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.

  • 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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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