In a recent paper (Temme, 2021) new asymptotic expansions are given for the Kummer functions M (a,b,z) and U (a,b + 1,z) for large positive values of a and b, with z fixed and special attention for the case a ~b . In this paper we extend the approach and also accept large values of z. The new expansions are valid when at least one of the parameters a, b, or z is large. We provide numerical tables to show the performance of the expansions.

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Indagationes Mathematicae
Scientific Computing

Temme, N., & Veling, E. J. M. (2022). Asymptotic expansions of Kummer hypergeometric functions with three asymptotic parameters a, b and z. Indagationes Mathematicae, 33(6), 1221–1235. doi:10.1016/j.indag.2022.08.001