  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.
