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1. CMB 2011 (vol 55 pp. 571)
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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 |