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Special Values of the Hypergeometric Series.

By: Material type: TextTextSeries: Memoirs of the American Mathematical SocietyPublisher: Providence : American Mathematical Society, 2017Copyright date: ©2017Edition: 1st edDescription: 1 online resource (108 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781470440565
Subject(s): Genre/Form: Additional physical formats: Print version:: Special Values of the Hypergeometric SeriesDDC classification:
  • 515/.5
LOC classification:
  • QA353.H9.E25 2017
Online resources:
Contents:
Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Preliminaries -- 2.1. Contiguity operators -- 2.2. Degenerate relations -- 2.3. A complete system of representatives of \\Z³ -- Chapter 3. Derivation of special values -- 3.1. Example 1: ( , , )=(0,1,1) -- 3.2. Example 2: ( , , )=(1,2,2) -- 3.3. Example 3: ( , , )=(1,2,3) -- Chapter 4. Tables of special values -- 4.1. =1 -- 4.2. =2 -- 4.3. =3 -- 4.4. =4 -- 4.5. =5 -- 4.6. =6 -- Appendix A. Some hypergeometric identities for generalized hypergeometric series and Appell-Lauricella hypergeometric series -- A.1. Some examples for generalized hypergeometric series -- A.2. Some examples for Appell-Lauricella hypereometric series -- Acknowledgments -- Bibliography -- Back Cover.
Summary: 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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Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Preliminaries -- 2.1. Contiguity operators -- 2.2. Degenerate relations -- 2.3. A complete system of representatives of \\Z³ -- Chapter 3. Derivation of special values -- 3.1. Example 1: ( , , )=(0,1,1) -- 3.2. Example 2: ( , , )=(1,2,2) -- 3.3. Example 3: ( , , )=(1,2,3) -- Chapter 4. Tables of special values -- 4.1. =1 -- 4.2. =2 -- 4.3. =3 -- 4.4. =4 -- 4.5. =5 -- 4.6. =6 -- Appendix A. Some hypergeometric identities for generalized hypergeometric series and Appell-Lauricella hypergeometric series -- A.1. Some examples for generalized hypergeometric series -- A.2. Some examples for Appell-Lauricella hypereometric series -- Acknowledgments -- Bibliography -- Back Cover.

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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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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