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

A. R. Miller, Richard B. Paris

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    15 Citations (Scopus)
    102 Downloads (Pure)

    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.
    Original languageEnglish
    Pages (from-to)31–45
    Number of pages15
    JournalZeitschrift fur Angewandte Mathematik und Physik
    Volume62
    Issue number1
    DOIs
    Publication statusPublished - Feb 2011

    Keywords

    • Generalized hypergeometric function
    • Euler transformation
    • Kummer transformation

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