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Special values of the hypergeometric series / Akihito Ebisu.

By: Material type: TextTextSeries: Memoirs of the American Mathematical Society ; v 248, no 1177.Publication details: Providence : American Mathematical Society, 2017.Description: 96 pages ; 25 cmISBN:
  • 9781470425333 (pbk : alk. paper)
Subject(s): DDC classification:
  • 510 23 Am512
Contents:
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 seriesA.2. Some examples for Appell-Lauricella hypereometric series; Acknowledgments; Bibliography.
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.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 510 Am512 (Browse shelf(Opens below)) Available 138219
Total holds: 0

Includes bibliographical references.

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 seriesA.2. Some examples for Appell-Lauricella hypereometric series; Acknowledgments; Bibliography.

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.

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