Error Bounds for the Large-Argument Asymptotic Expansions of the Hankel and Bessel Functions View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2017-08

AUTHORS

Gergő Nemes

ABSTRACT

In this paper, we reconsider the large-argument asymptotic expansions of the Hankel, Bessel and modified Bessel functions and their derivatives. New integral representations for the remainder terms of these asymptotic expansions are found and used to obtain sharp and realistic error bounds. We also give re-expansions for these remainder terms and provide their error estimates. A detailed discussion on the sharpness of our error bounds and their relation to other results in the literature is given. The techniques used in this paper should also generalize to asymptotic expansions which arise from an application of the method of steepest descents. More... »

PAGES

141-177

References to SciGraph publications

  • 1973. Tables of Laplace Transforms in NONE
  • 1890-09. Zur Theorie der Bessel'schen Functionen in MATHEMATISCHE ANNALEN
  • 1869-09. Die Cylinderfunctionen erster und zweiter Art in MATHEMATISCHE ANNALEN
  • Journal

    TITLE

    Acta Applicandae Mathematicae

    ISSUE

    1

    VOLUME

    150

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10440-017-0099-0

    DOI

    http://dx.doi.org/10.1007/s10440-017-0099-0

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1085428172


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