Exponentially small expansions in the asymptotics of the Wright function

Richard B. Paris

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    20 Citations (Scopus)
    97 Downloads (Pure)

    Abstract

    We consider exponentially small expansions present in the asymptotics of the generalised hypergeometric function, or Wright function, pΨq(z) for large |z| that have not been considered in the existing theory. Our interest is principally with those functions of this class that possess either a finite algebraic expansion or no such expansion and with parameter values that produce exponentially small expansions in the neighbourhood of the negative real z axis. Numerical examples are presented to demonstrate the presence of these exponentially small expansions.
    Original languageEnglish
    Pages (from-to)488-504
    Number of pages17
    JournalJournal of Computational and Applied Mathematics
    Volume234
    Issue number2
    DOIs
    Publication statusPublished - May 2010

    Keywords

    • Asymptotics
    • Wright function
    • Exponentially small expansions
    • Generalised hypergeometric functions

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