Multiplicate inverse forms of terminating hypergeometric series
Abstract
The multiplicate form of Gould--Hsu's inverse series relations enables to investigate the dual relations of the Chu-Vandermonde-Gau{\ss}'s, the Pfaff-Saalsch\"utz's summation theorems and the binomial convolution formula due to Hagen and Rothe. Several identitity and reciprocal relations are thus established for terminating hypergeometric series. By virtue of the duplicate inversions, we establish several dual formulae of Chu-Vandermonde-Gau{\ss}'s and Pfaff-Saalsch\"utz's summation theorems in Section (3)\cite{ChuVanGauss} and (4)\cite{PfaffSaalsch}, respectively. Finally, the last section is devoted to deriving several identities and reciprocal relations for terminating balanced hypergeometric series from Hagen-Rothe's convolution identity in accordance with the duplicate, triplicate and multiplicate inversions.
Cite
@article{arxiv.1311.4502,
title = {Multiplicate inverse forms of terminating hypergeometric series},
author = {Christian Lavault},
journal= {arXiv preprint arXiv:1311.4502},
year = {2013}
}
Comments
15 pages