Computation of parabolic cylinder functions having complex argument
Numerical methods for the computation of the parabolic cylinder function U(a,z) for real a and complex z are presented. The main tools are recent asymptotic expansions involving exponential and Airy functions, with slowly varying analytic coefficient functions involving simple coefficients, and stab...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universidad de Cantabria (UC) |
| Repositorio: | UCrea Repositorio Abierto de la Universidad de Cantabria |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.unican.es:10902/31000 |
| Acceso en línea: | https://hdl.handle.net/10902/31000 |
| Access Level: | acceso abierto |
| Palabra clave: | Parabolic cylinder functions Asymptotic expansions Numerical quadrature Numerical algorithms |
| Sumario: | Numerical methods for the computation of the parabolic cylinder function U(a,z) for real a and complex z are presented. The main tools are recent asymptotic expansions involving exponential and Airy functions, with slowly varying analytic coefficient functions involving simple coefficients, and stable integral representations; these two main methods can be complemented with Maclaurin series and a Poincaré asymptotic expansion. We provide numerical evidence showing that the combination of these methods is enough for computing the function with 5 × 10-13 relative accuracy in double precision floating point arithmetic. |
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