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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 language | English |
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Pages (from-to) | 141-177 |
Number of pages | 37 |
Journal | Acta Applicandae Mathematicae |
Volume | 150 |
Issue number | 1 |
Early online date | 17 May 2017 |
DOIs | |
Publication status | Published - Aug 2017 |
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Dive into the research topics of 'Error bounds for the large-argument asymptotic expansions of the Hankel and Bessel functions'. Together they form a unique fingerprint.Projects
- 1 Finished
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Rigorous and Presentable Asymptotics for Special Functions and Orthogonal Polynomials
1/09/15 → 31/08/20
Project: Research