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Special Values of the Hypergeometric Series.

Ebisu, Akihito.

Special Values of the Hypergeometric Series. - 1st ed. - 1 online resource (108 pages) - Memoirs of the American Mathematical Society ; v.248 . - Memoirs of the American Mathematical Society .

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.

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.

9781470440565


Hypergeometric series.


Electronic books.

QA353.H9.E25 2017

515/.5

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