A generalization of Kummer's identity
摘要
The well-known Kummer's formula evaluates the hypergeometric series 2F1(A,B;C;-1) when the relation B-A+C=1 holds. This paper deals with evaluation of 2F1(-1) series in the case when C-A+B is an integer. Such a series is expressed as a sum of two \Gamma-terms multiplied by terminating 3F2(1) series. A few such formulas were essentially known to Whipple in 1920's. Here we give a simpler and more complete overview of this type of evaluations. Additionally, algorithmic aspects of evaluating hypergeometric series are considered. We illustrate Zeilberger's method and discuss its applicability to non-terminating series, and present a couple of similar generalizations of other known formulas.
引用
@article{arxiv.math/0005095,
title = {A generalization of Kummer's identity},
author = {Raimundas Vidunas},
journal= {arXiv preprint arXiv:math/0005095},
year = {2007}
}
备注
13 pages; classical proofs simplified, possible transformations reviewed; in the algoritmic part similar evaluations of other series added