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arXiv · 1707.08175

Error bounds for the large-argument asymptotic expansions of the Lommel and allied functions

Gergő Nemes
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Abstract

In this paper, we reconsider the large-$z$ asymptotic expansion of the Lommel function $S_{\mu,\nu}(z)$ and its derivative. New representations for the remainder terms of the 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. Applications to the asymptotic expansions of the Anger--Weber-type functions, the Scorer functions, the Struve functions and their derivatives are provided. The sharpness of our error bounds is discussed in detail, and numerical examples are given.

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BibTeXRIS

Gergő Nemes. 2017-07-22. Error bounds for the large-argument asymptotic expansions of the Lommel and allied functions. https://doi.org/10.1111/sapm.12210

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