TY  - BOOK
AU  - Ebisu,Akihito
TI  - Special values of the hypergeometric series
T2  - Memoirs of the American Mathematical Society
SN  - 9781470425333 (pbk : alk. paper)
U1  - 510 23
PY  - 2017///
CY  - Providence
PB  - American Mathematical Society
KW  - Hypergeometric series
KW  - Cohen-Macaulay modules
KW  - Modules (Algebra)
KW  - Singularities (Mathematics)
N1  - 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
N2  - 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
ER  -