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# A Generalised Kummer-Type Transformation for the ${}_pF_p(x)$ Hypergeometric Function

Published:2011-05-17
Printed: Sep 2012
• A. R. Miller,
Department of Mathematics, George Washington University, Washington, DC 20009-2525, USA
• R. B. Paris,
Division of Complex Systems, University of Abertay Dundee, Dundee DD1 1HG, UK
 Format: LaTeX MathJax PDF

## Abstract

In a recent paper, Miller derived a Kummer-type transformation for the generalised hypergeometric function ${}_pF_p(x)$ when pairs of parameters differ by unity, by means of a reduction formula for a certain Kampé de Fériet function. An alternative and simpler derivation of this transformation is obtained here by application of the well-known Kummer transformation for the confluent hypergeometric function corresponding to $p=1$.
 Keywords: generalised hypergeometric series, Kummer transformation
 MSC Classifications: 33C15 - Confluent hypergeometric functions, Whittaker functions, ${}_1F_1$ 33C20 - Generalized hypergeometric series, ${}_pF_q$

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