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Euler-type transformations for the generalized hypergeometric function r+2 F r+1(x)

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Abstract

We provide generalizations of two of Euler’s classical transformation formulas for the Gauss hypergeometric function extended to the case of the generalized hypergeometric function r+2 F r+1(x) when there are additional numeratorial and denominatorial parameters differing by unity. The method employed to deduce the latter is also implemented to obtain a Kummer-type transformation formula for r+1 F r+1 (x) that was recently derived in a different way.

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Authors and Affiliations

  1. 1616 18th Street NW, Washington, DC, 20009-2525, USA

    A. R. Miller

  2. Division of Complex Systems, University of Abertay Dundee, Dundee, DD1 1HG, UK

    R. B. Paris

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  1. A. R. Miller
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  2. R. B. Paris
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Correspondence to A. R. Miller.

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Miller, A.R., Paris, R.B. Euler-type transformations for the generalized hypergeometric function r+2 F r+1(x). Z. Angew. Math. Phys. 62, 31–45 (2011). https://doi.org/10.1007/s00033-010-0085-0

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  • DOI: https://doi.org/10.1007/s00033-010-0085-0

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