Exponentially small expansions of the confluent hypergeometric functions

Richard B. Paris

    Research output: Contribution to journalArticlepeer-review

    7 Citations (Scopus)
    123 Downloads (Pure)

    Abstract

    The asymptotic expansions of the confluent hypergeometric functions 1F1(a; b; z) and U(a, b, z) are examined as |z|→∞ on the Stokes lines arg z = ±π. Particular attention is given to the exponentially small contributions associated with these two functions. Numerical results demonstrating the accuracy of the expansions are given.
    Original languageEnglish
    Pages (from-to)6601-6609
    Number of pages9
    JournalApplied Mathematical Sciences
    Volume7
    Issue number133
    DOIs
    Publication statusPublished - 2013

    Keywords

    • Confluent hypergeometric functions
    • Stokes lines
    • Asymptotic expansions
    • Exponentially small expansions

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