The Asymptotic Expansion of Kummer Functions for Large Values of the α-Parameter, and Remarks on a Paper by Olver - Volkmer, H. (Symmetry, Integrability and Geometry: Methods and Applications, 2016)
It is shown that a known asymptotic expansion of the Kummer function U(a,b,z) as a tends to infinity is valid for z on the full Riemann surface of the logarithm. A corresponding result is also proved in a more general setting considered by Olver (1956).