On the large argument asymptotics of the Lommel function via Stieltjes transforms

Abstract

The aim of this paper is to investigate in detail the known large argument asymptotic series of the Lommel function by Stieltjes transform representations. We obtain a number of properties of this asymptotic expansion, including explicit and realistic error bounds, exponentially improved asymptotic expansions, and the smooth transition of the Stokes discontinuities. An interesting consequence related to the large argument asymptotic series of the Struve function is also proved.

20 pages

Cited by in corpus (2)

• Estimates of the asymptotic Nikolskii constants for spherical polynomials
• Uniform asymptotic expansions for Lommel, Anger-Weber and Struve functions