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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.
Journal of Computational Physics


Abramowitz functions, least squares method, Laurent series


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], (Accessed April 23, 2024)
Created March 15, 2020, Updated May 15, 2020