New asymptotic expansions are derived of the Kummer functions M(a, b, z) and U(a, b+1, z) for large positive values of a and b, with z fixed. For both functions we consider b/a <= 1 and b/a >= 1, with special attention for the case a ~ b. We use a uniform method to handle all cases of these parameters.

Asymptotic expansions, Confluent hypergeometric functions, Kummer functions
Integral Transforms and Special Functions
Centrum Wiskunde & Informatica, Amsterdam, The Netherlands

Temme, N.M. (2021). Asymptotic expansions of Kummer hypergeometric functions for large values of the parameters. Integral Transforms and Special Functions. doi:10.1080/10652469.2021.1886094