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Computation of parabolic cylinder functions having complex argument

Abstract: 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.

 Autoría: Dunster T.M., Gil A., Segura J.,

 Fuente: Applied Numerical Mathematics, 2024, 197, 230-242

 Editorial: Elsevier

 Fecha de publicación: 01/03/2024

 Nº de páginas: 13

 Tipo de publicación: Artículo de Revista

 DOI: 10.1016/j.apnum.2023.11.017

 ISSN: 0168-9274,1873-5460

 Proyecto español: PGC2018-098279-B-I00

 Url de la publicación: https://doi.org/10.1016/j.apnum.2023.11.017