# Error Bounds for the Large‐Argument Asymptotic Expansions of the Lommel and Allied Functions

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In this paper, we reconsider the large‐z asymptotic expansion of the Lommel function ${S}_{\mu ,\nu }\left(z\right)$ 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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Document Type: Research Article

Publication date: May 1, 2018

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