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

06/28/2019

∙

by   Zydrunas Gimbutas, et al.

∙

0

∙

share

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 precision, 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.