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

In this paper, we reconsider the large-z asymptotic expansion of the Lommel function S_μ,ν (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.