  Using a differential equation approach asymptotic expansions are rigorously
obtained for Lommel, Weber, Anger-Weber and Struve functions, as well as
Neumann polynomials, each of which is a solution of an inhomogeneous Bessel
equation. The approximations involve Airy and Scorer functions, and are
uniformly valid for large real order $\nu$ and unbounded complex argument $z$.
An interesting complication is the identification of the Lommel functions with
the new asymptotic solutions, and in order to do so it is necessary to consider
certain sectors of the complex plane, as well as introduce new forms of Lommel
and Struve functions.
