On nonoscillating integrals for computing inhomogeneous Airy functions

Integral representations are considered of solutions of the inhomogeneous A iry differential equation w'' - z w = +/- 1/pi. The solutions of these equa tions are also known as Scorer functions. Certain functional relations for these functions are used to confine the discussion to one function and to a certain sector in the complex plane. By using steepest descent methods fro m asymptotics, the standard integral representations of the Scorer function s are modified in order to obtain nonoscillating integrals for complex valu es of z. In this way stable representations for numerical evaluations of th e functions are obtained. The methods are illustrated with numerical result s.