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

Abstract

The aim of this paper is to investigate 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, and an exponentially improved asymptotic expansion. An interesting consequence related to the large argument asymptotic series of the Struve function is also proved.