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

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.