  In this paper, we derive a new representation for the Anger--Weber function,
employing the reformulation of the method of steepest descents by C. J. Howls
(Howls, Proc. R. Soc. Lond. A 439 (1992) 373--396). As a consequence of this
representation, we deduce a number of properties of the large order asymptotic
expansion of the Anger--Weber function, including explicit and realistic error
bounds, asymptotic approximations for the late coefficients, exponentially
improved asymptotic expansions, and the smooth transition of the Stokes
discontinuities.

Classical Analysis and ODEs