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Zbl 0972.33004
Gil, Amparo; Segura, Javier; Temme, Nico M.
On nonoscillating integrals for computing inhomogeneous Airy functions. (English)
[J] Math. Comput. 70, No.235, 1183-1194 (2001). ISSN 0025-5718; ISSN 1088-6842/e

Integral representations are considered of solutions of the inhomogeneous Airy differential equation $w''-z w=\pm 1/\pi$. The solutions of these equations are also known as Scorer functions. By using steepest descent methods from asymptotics, the standard integral representations of the Scorer functions are modified in order to obtain non-oscillating integrals for complex values of $z$. In this way stable representations for numerical evaluations of the functions are obtained. The methods are illustrated with numerical results.
[N.M.Temme (Amsterdam)]

MSC 2000:: *33C10 Cylinder functions, etc.
41A60 Asymptotic problems in approximation
30E10 Approximation in the complex domain
65D20 Computation of special functions

Keywords: inhomogeneous Airy functions; Scorer functions; method of steepest descent; computation of special functions

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