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

Error Bounds for the Large-Argument Asymptotic Expansions of the Hankel and Bessel Functions 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

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

Acta Applicandae Mathematicae , Volume 150 (1) – May 17, 2017

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References (45)

Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer Science+Business Media Dordrecht
Subject
Mathematics; Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Classical Mechanics
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/s10440-017-0099-0
Publisher site
See Article on Publisher Site

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.

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: May 17, 2017

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