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