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

Gergo Nemes

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we reconsider the large-z asymptotic expansion of the Lommel function Sμ,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.
Original languageEnglish
Pages (from-to)508-541
Number of pages34
JournalStudies in Applied Mathematics
Volume140
Issue number4
Early online date22 Feb 2018
Publication statusPublished - May 2018

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