Computation of parabolic cylinder functions having complex argument
DOI10.1016/j.apnum.2023.11.017arXiv2210.16982OpenAlexW4388933952MaRDI QIDQ6131512
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Publication date: 5 April 2024
Published in: Applied Numerical Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2210.16982
Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Computation of special functions and constants, construction of tables (65D20) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Numerical approximation and evaluation of special functions (33F05) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)
Cites Work
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- Computation of asymptotic expansions of turning point problems via Cauchy's integral formula: Bessel functions
- Integral representations for computing real parabolic cylinder functions
- Algorithm 914
- Fast and accurate computation of the Weber parabolic cylinder function W(a, x)
- Asymptotic Methods for Integrals
- Computing the real parabolic cylinder functions U ( a , x ), V ( a , x )
- Algorithm 850
- Second-order linear differential equations with two turning points
- Algorithm 644
- Simplified error bounds for turning point expansions
- Nield--Kuznetsov Functions and Laplace Transforms of Parabolic Cylinder Functions
- Algorithm 819: AIZ, BIZ
- Uniform asymptotic expansions for solutions of the parabolic cylinder and Weber equations
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