Parabolic cylinder functions of large order

D. S. Jones

    Research output: Contribution to journalArticlepeer-review

    2 Citations (Scopus)

    Abstract

    The asymptotic behaviour of parabolic cylinder functions of large real order is considered. Various expansions in terms of elementary functions are derived. They hold uniformly for the variable in appropriate parts of the complex plane. Some of the expansions are doubly asymptotic with respect to the order and the complex variable which is an advantage for computational purposes. Error bounds are determined for the truncated versions of the asymptotic series.
    Original languageEnglish
    Pages (from-to)453-469
    Number of pages17
    JournalJournal of Computational and Applied Mathematics
    Volume190
    Issue number1-2
    DOIs
    Publication statusPublished - 2006

    Keywords

    • Parabolic cylinder functions
    • Uniform asymptotic expansions
    • Computation of special functions

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