TY  - BOOK
AU  - Ebisu,Akihito
TI  - Special Values of the Hypergeometric Series
T2  - Memoirs of the American Mathematical Society
SN  - 9781470440565
AV  - QA353.H9.E25 2017 
U1  - 515/.5 
PY  - 2017///
CY  - Providence
PB  - American Mathematical Society
KW  - Hypergeometric series
KW  - Electronic books
N1  - 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
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 and finds that this set includes almost all previously known values and many previously unknown values
UR  - https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4940245
ER  -