Special values of the hypergeometric series

Special values of the hypergeometric series

by Ebisu, Akihito

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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 t…

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Title Statements

  • Full title :Special values of the hypergeometric series / Akihito Ebisu.

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 p.

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Edition Statements

  • Publication Date:2017

Publication Statements

Notes

Titre de l'écran-titre (visionné le 5 décembre 2017).

In AMS.

"Volume 248, number 1177 (third of 5 numbers), July 2017."

The Physical Object

  • Description:1 ressource en ligne (v, 96 pages) : : fichier PDF

Edition Identifiers

  • ISBN:9781470440565, 1470440563
  • oclc:on1028651159
  • LC Classification:QA353.H9
  • Dewey Decimal:515/.5

Table of 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 seriesA.2. Some examples for Appell-Lauricella hypereometric series; Acknowledgments; Bibliography; Back Cover

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Subjects

Cohen-Macaulay modules Hypergeometric series Modules (Algebra) Modules (Algèbre) Modules de Cohen-Macaulay Séries hypergéométriques Singularités (Mathématiques) Singularities (Mathematics)

Writers

Ebisu, Akihito

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