On nonoscillating integrals for computing inhomogeneous Airy functions
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- by Amparo Gil, Javier Segura and Nico M. Temme PDF
- Math. Comp. 70 (2001), 1183-1194 Request permission
Abstract:
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. 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 $z$. In this way stable representations for numerical evaluations of the functions are obtained. The methods are illustrated with numerical results.References
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Additional Information
- Amparo Gil
- Affiliation: Instituto de Bioingeniería, Universidad Miguel Hernández, Edificio La Galia. 03202-Elche (Alicante), Spain
- Email: amparo@titan.ific.uv.es
- Javier Segura
- Affiliation: Instituto de Bioingeniería, Universidad Miguel Hernández, Edificio La Galia. 03202-Elche (Alicante), Spain
- MR Author ID: 627158
- Email: segura@flamenco.ific.uv.es
- Nico M. Temme
- Affiliation: CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands
- Email: nicot@cwi.nl
- Received by editor(s): September 11, 1998
- Received by editor(s) in revised form: April 27, 1999, and August 25, 1999
- Published electronically: April 13, 2000
- © Copyright 2000 American Mathematical Society
- Journal: Math. Comp. 70 (2001), 1183-1194
- MSC (2000): Primary 33C10, 41A60, 30E10, 65D20
- DOI: https://doi.org/10.1090/S0025-5718-00-01268-0
- MathSciNet review: 1826580