Evaluation of Abramowitz functions in the right half of the complex plane
Zydrunas Gimbutas, Shidong Jiang, Li-Shi Luo
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.
, Jiang, S.
and Luo, L.
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 October 27, 2021)