Asymptotic expansions of the Whittaker functions for large order parameter

Abstract

The asymptotic behavior of the Whittaker functions M^^z) and W Ki n(z) for large modulus of the parameter K is considered. Asymptotic expansions in descending powers of ^/K are derived. The ^-independent coefficients of these expansions can be calculated in a simple way, making these approximations quite useful in practice. An explicit error bound for the expansion of M K , }fl (z) also is obtained.