Certain summation and transformation formulas for generalized hypergeometric series

Authors:
Allen R. Miller
Affiliations:
Formerly Professor of Mathematics at George Washington University, 1616 18th Street NW #210, Washington, DC 20009-2525, USA
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

We derive summation formulas for generalized hypergeometric series of unit argument, one of which upon specialization reduces to Minton's summation theorem. As an application we deduce a reduction formula for a certain Kampe de Feriet function that in turn provides a Kummer-type transformation formula for the generalized hypergeometric function "pF"p(x).