In Slater's 1960 standard work on confluent hypergeometric functions, also called Kummer functions, a number of asymptotic expansions of these functions can be found. We summarize expansions derived from a differential equation for large values of the $a-$parameter. We show how similar expansions can be derived by using integral representations, and we observe discrepancies with Slater's expansions.

Additional Metadata
Keywords Asymptotic analysis, Kummer functions, confluent hypergeometric functions, Bessel functions
MSC Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) (msc 33B20), Confluent hypergeometric functions, Whittaker functions, ${}_1F_1$ (msc 33C15), Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (msc 41A60), Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) (msc 33B20)
THEME Other (theme 6)
Note Proceedings of the International Conference on Differential Equations, Difference Equations and Special Functions, Patras, Greece, September 3 - 9, 2012, dedicated to the memory of Panayiotis D. Siafarikas.
Citation
Temme, N.M. (2013). Remarks on Slater's asymptotic expansions of Kummer functions for large values of the $a-$parameter.