On nonoscillating integrals for computing inhomogeneous Airy functions

DOI10.1090/S0025-5718-00-01268-0zbMath0972.33004arXivmath/0109187OpenAlexW2038463664MaRDI QIDQ2719072

Amparo Gil, Javier Segura, Nico M. Temme

Publication date: 14 May 2001

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0109187

zbMATH Keywords

computation of special functionsmethod of steepest descentScorer functionsinhomogeneous Airy functions

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Approximation in the complex plane (30E10) Computation of special functions and constants, construction of tables (65D20) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10)

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Uses Software

• Algorithm 644

Cites Work

• Numerical evaluation of Airy functions with complex arguments
• An algorithm for the evaluation of the complex Airy functions
• Computation of inhomogeneous Airy functions
• Steepest descent paths for integrals defining the modified Bessel functions of imaginary order
• NUMERICAL EVALUATION OF INTEGRALS OF THE FORM Formula AND THE TABULATION OF THE FUNCTION Formula
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