Clausen's series 3F2(1) with integral parameter differences and transformations of the hypergeometric function 2F2(x)

A. R. Miller, Richard B. Paris

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    9 Citations (Scopus)
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    Abstract

    We obtain summation formulas for the hypergeometric series 3 F 2(1) with at least one pair of numeratorial and denominatorial parameters differing by a negative integer. The results derived for the latter are used to obtain Kummer-type transformations for the generalized hypergeometric function 2 F 2(x) and reduction formulas for certain Kampé de Fériet functions. Certain summations for the partial sums of the Gauss hypergeometric series 2 F 1(1) are also obtained.
    Original languageEnglish
    Pages (from-to)21-33
    Number of pages13
    JournalIntegral Transforms and Special Functions
    Volume23
    Issue number1
    DOIs
    Publication statusPublished - 2012

    Keywords

    • Kummer-type transformation
    • Generalized hypergeometric function
    • Summation and reduction formula
    • Partial sums of the Gauss function at unit argument

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