On two Thomae-type transformations for hypergeometric series with integral parameter differences

Yong Sup Kim; Arjun Rathie; Richard Bruce Paris

Vol. 19 No. 1 (2014)

Regular Articles

On two Thomae-type transformations for hypergeometric series with integral parameter differences

Published 2014-02-06

Yong Sup Kim
Arjun Rathie
Richard Bruce Paris

Yong Sup Kim
Dept Mathematics Education Wonkwang University

Arjun Rathie
Dept mathematics Central University of Kerala

Richard Bruce Paris
University of Abertay Dundee

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Abstract

We obtain two new Thomae-type transformations for hypergeometric series with $r$ pairs of numeratorial and denominatorial parameters differing by positive integers. This is achieved by application of the so-called Beta integral method developed by Krattenthaler and Rao [Symposium on Symmetries in Science (ed. B. Gruber), Kluwer (2004)] to two recently obtained Euler-type transformations. Some special cases are given.

Keywords

generalized hypergeometric series, Thomae transformations, generalized Euler-type transformations

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Author Biography

Yong Sup Kim

Professor

Arjun Rathie

Professor

Richard Bruce Paris

School of Engineering, Computing and Applied Mathematics

Emeritus Reader