Gimbutas, Z.
, Jiang, S.
and Luo, L.
(2020),
Evaluation of Abramowitz functions in the right half of the complex plane, Journal of Computational Physics, [online], https://doi.org/10.1016/j.jcp.2019.109169 (Accessed May 7, 2026)
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
Secure .gov websites use HTTPS
A lock (
) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.
Evaluation of Abramowitz functions in the right half of the complex plane
Published
Author(s)
, Shidong Jiang, Li-Shi Luo
Abstract
A numerical scheme is developed for the evaluation of Abramowitz functions J n in the right half of the complex plane. For n = −1, . . . , 2, the scheme utilizes series expansions for |z| < 1 and asymptotic expansions for |z| > R with R determined by the required accuracy, and modified Laurent series expansions which are precomputed via a least squares procedure to approximate J n accurately and efficiently on each sub-region in the intermediate region 1 ≤ |z| ≤ R. For n > 2, J n is evaluated via a recurrence relation. The scheme achieves nearly machine precision for n = −1, . . . , 2, with the cost about four times of evaluating a complex exponential per function evaluation.Citation
Journal of Computational Physics
Pub Type
Journals
Download Paper
Keywords
Abramowitz functions, least squares method, Laurent series
Citation
Issues
If you have any questions about this publication or are having problems accessing it, please contact [email protected].
Created March 15, 2020, Updated May 15, 2020