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1. CMB 2011 (vol 55 pp. 571)

Miller, A. R.; Paris, R. B.
A Generalised Kummer-Type Transformation for the ${}_pF_p(x)$ Hypergeometric Function
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
Categories:33C15, 33C20

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