  Asymptotic expansions are derived for solutions of the parabolic cylinder and
Weber differential equations. In addition the inhomogeneous versions of the
equations are considered, for the case of polynomial forcing terms. The
expansions involve exponential, Airy and Scorer functions and slowly varying
analytic coefficient functions involving simple coefficients. The
approximations are uniformly valid for large values of the parameter and
unbounded real and complex values of the argument. Explicit and readily
computable error bounds are either furnished or available for all
approximations.
