Transformation formulas for the generalized hypergeometric function with integral parameter differences

A. R. Miller, Richard B. Paris

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    26 Citations (Scopus)
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    Abstract

    Transformation formulas of Euler and Kummer-type are derived respectively for the generalized hypergeometric functions r+2Fr+1(x) and r+1Fr+1(x), where r pairs of numeratorial and denominatorial parameters differ by positive integers. Certain quadratic transformations for the former function, as well as a summation theorem when x = 1, are also considered.
    Original languageEnglish
    Pages (from-to)291-327
    Number of pages37
    JournalRocky Mountain Journal of Mathematics
    Volume43
    Issue number1
    DOIs
    Publication statusPublished - 2013

    Keywords

    • Generalized hypergeometric function
    • Euler transformation
    • Kummer transformation
    • Quadratic transformations
    • Summation theorem
    • Zeros of entire functions

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