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. A detailed discussion on the sharpness of our error bounds and numerical examples are also given.