1. Evaluation of Abramowitz functions in the right half of the complex plane
- Author
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Gimbutas, Zydrunas, Jiang, Shidong, and Luo, Li-Shi
- Subjects
Mathematics - Numerical Analysis ,33E20, 33F05, 65D15, 65E05, 65F99 - Abstract
A numerical scheme is developed for the evaluation of Abramowitz functions $J_n$ in the right half of the complex plane. For $n=-1,\, \ldots,\, 2$, 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 $1\le |z| \le R$. For $n>2$, $J_n$ is evaluated via a recurrence relation. The scheme achieves nearly machine precision for $n=-1, \ldots, 2$, with the cost about four times of evaluating a complex exponential per function evaluation., Comment: 24 pages, 2 figures
- Published
- 2019
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