Expansions in terms of Bessel functions are considered of the Kummer function ${}_1F_1(a;c,z)$ (or confluent hypergeometric function) as given by Tricomi and Buchholz. The coefficients of these expansions are polynomials in the parameters of the Kummer function and the asymptotic behavior of these polynomials for large degree is given. Tables are given to show the rate of approximation of the asymptotic estimates. The numerical performance of the expansions is discussed together with the numerical stability of recurrence relations to compute the polynomials. The asymptotic character of the expansions is explained for large values of the parameter $a$ of the Kummer function.

Kummer functions, confluent hypergeometric functions, Bessel functions, asymptotic expansions, computation of special functions.
Bessel and Airy functions, cylinder functions, ${}_0F_1$ (msc 33C10)
Springer
Numerische Mathematik
DOI 10.1007/s00211-010-0303-x

López, J.L, & Temme, N.M. (2010). Asymptotics and Numerics of Polynomials Used in Tricomi and Buchholz Expansions of Kummer functions. Numerische Mathematik.