Evaluation of Abramowitz functions in the right half of the complex plane

Document Type

Article

Publication Date

3-15-2020

Abstract

A numerical scheme is developed for the evaluation of Abramowitz functions Jn in the right half of the complex plane. For n=−1,…,2, the scheme utilizes series expansions for |z|<1, asymptotic expansions for |z|>R with R determined by the required precision, and least squares Laurent polynomial approximations on each sub-region in the intermediate region 1≤|z|≤R. For n>2, Jn is evaluated via a forward recurrence relation. The scheme achieves nearly machine precision for n=−1,…,2 at a cost that is competitive as compared with software packages for the evaluation of other special functions in the complex domain.

Identifier

85078010856 (Scopus)

Publication Title

Journal of Computational Physics

External Full Text Location

https://doi.org/10.1016/j.jcp.2019.109169

e-ISSN

10902716

ISSN

00219991

Volume

405

Grant

1720405

Fund Ref

National Institute of Standards and Technology

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