Asymptotics of the Gauss hypergeometric function with large parameters, II

Richard B. Paris

    Research output: Contribution to journalArticlepeer-review

    73 Downloads (Pure)

    Abstract

    We obtain asymptotic expansions by application of the method of steepest descents for the Gauss hypergeometric function F(a+ε1λ,b+ε2λ;c+λ;z) as |λ| → ∞ when 0<ε1 <1 and ε1 >1 where, without loss of generality, it is supposed that ε1 6ε2 . The resulting expansions are of Poincar´e type and break down in the neighbourhood of certain critical points in the z-plane. Numerical results illustrating the accuracy of the different expansions are given.
    Original languageEnglish
    Pages (from-to)1-15
    Number of pages15
    JournalJournal of Classical Analysis
    Volume3
    Issue number1
    Publication statusPublished - 2013

    Keywords

    • Hypergeometric functions
    • Asymptotic expansion
    • Large parameters

    Fingerprint

    Dive into the research topics of 'Asymptotics of the Gauss hypergeometric function with large parameters, II'. Together they form a unique fingerprint.

    Cite this