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Integral representations are considered of solutions of the inhomo- geneous Airy dierential equation w00 zw=1=. The solutions of these equations are also known as Scorer functions. Certain functional relations for these functions are used to conne the discussion to one function and to a certain sector in the complex plane. By using steepest descent methods from asymptotics, the standard integral representations of the Scorer functions are modied in order to obtain nonoscillating integrals for complex values of z .I n this way stable representations for numerical evaluations of the functions are obtained. The methods are illustrated with numerical results.

On nonoscillating integrals for computing inhomogeneous Airy functions