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A Generalised Kummer-Type Transformation for the pFp(x) Hypergeometric Function

Published online by Cambridge University Press:  20 November 2018

A. R. Miller  and
R. B. Paris
A. R. Miller
Affiliation:
Department of Mathematics, George Washington University, Washington, DC 20009-2525, USAe-mail: r.paris@abertay.ac.uk
R. B. Paris
Affiliation:
Division of Complex Systems, University of Abertay Dundee, Dundee DD1 1HG, UK
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Abstract

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In a recent paper, Miller derived a Kummer-type transformation for the generalised hypergeometric function $_{p}{{F}_{p}}(x)$ 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

33C1533C20generalised hypergeometric seriesKummer transformation
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 55 , Issue 3 , 01 September 2012 , pp. 571 - 578
Copyright
Copyright © Canadian Mathematical Society 2012

References

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