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On nonoscillating integrals for computing inhomogeneous Airy functions |
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| Authors: | Amparo Gil Javier Segura Nico M Temme |
| Institution: | Instituto de Bioingeniería, Universidad Miguel Hernández, Edificio La Galia. 03202-Elche (Alicante), Spain ; Instituto de Bioingeniería, Universidad Miguel Hernández, Edificio La Galia. 03202-Elche (Alicante), Spain ; CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands |
| Abstract: | Integral representations are considered of solutions of the inhomogeneous Airy differential equation |
| Keywords: | Inhomogeneous Airy functions Scorer functions method of steepest descent saddle point method numerical computation of special functions |
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. The solutions of these equations 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 from asymptotics, the standard integral representations of the Scorer functions are modified in order to obtain nonoscillating integrals for complex values of 
. In this way stable representations for numerical evaluations of the functions are obtained. The methods are illustrated with numerical results.