Error bounds for the large-argument asymptotic expansions of the Hankel and Bessel functions

Gergo Nemes

Research output: Contribution to journalArticlepeer-review

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.
Original languageEnglish
Pages (from-to)141-177
Number of pages37
JournalActa Applicandae Mathematicae
Volume150
Issue number1
Early online date17 May 2017
DOIs
Publication statusPublished - Aug 2017

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