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.

Additional Metadata
Keywords Kummer functions, confluent hypergeometric functions, Bessel functions, asymptotic expansions, computation of special functions.
MSC Bessel and Airy functions, cylinder functions, ${}_0F_1$ (msc 33C10)
Publisher Springer
Journal Numerische Mathematik
Note DOI 10.1007/s00211-010-0303-x
Citation
López, J.L, & Temme, N.M. (2010). Asymptotics and Numerics of Polynomials Used in Tricomi and Buchholz Expansions of Kummer functions. Numerische Mathematik.