Title: Error bounds for the large-argument asymptotic expansions of the Hankel and Bessel functions
(Submitted on 25 Jun 2016 (v1), last revised 2 Mar 2017 (this version, v2))
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.
Submission historyFrom: Gergő Nemes [view email]
[v1] Sat, 25 Jun 2016 20:22:06 GMT (27kb)
[v2] Thu, 2 Mar 2017 12:17:19 GMT (36kb)
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