Special Values of the Hypergeometric Series

Akihito Ebisu (Autor)

Buch | Softcover

96 Seiten

2017
American Mathematical Society (Verlag)
978-1-4704-2533-3 (ISBN)

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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 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.

Akihito Ebisu, Hokkaido University, Sapporo, Japan.

Introduction
Preliminaries
Derivation of special values
Tables of special values
Appendix A. Some hypergeometric identities for generalized hypergeometric series and Appell-Lauricella hypergeometric series
Acknowledgments
Bibliography.

Erscheinungsdatum	12.08.2017
Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Gewicht	180 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
ISBN-10	1-4704-2533-5 / 1470425335
ISBN-13	978-1-4704-2533-3 / 9781470425333
Zustand	Neuware