Asymptotic expansions of Kummer hypergeometric functions with three asymptotic parameters a, b and z

2022/02/25 by Temme, N. M., Veling, E. J. M. · 1 citation
#33C15 #41A60 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #G.0 #G.1

paper · doi:10.48550/arxiv.2202.12857

Abstract

In a recent paper \citeTemme:2021:AKH 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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