  The aim of this paper is to derive new representations for the Anger--Weber
function, exploiting the reformulation of the method of steepest descents by C.
J. Howls (Howls, Proc. R. Soc. Lond. A 439 (1992) 373--396). Using these
representations, we obtain a number of properties of the large order asymptotic
expansions of the Anger--Weber function, including explicit and realistic error
bounds, asymptotics for the late coefficients, exponentially improved
asymptotic expansions, and the smooth transition of the Stokes discontinuities.
