Asymptotic expansions of the Whittaker functions for large order parameter

Abstract. The asymptotic behavior of the Whittaker functions Mκ, μ(z) and Wκ, μ(z) for large modulus of the parameter κ is considered. Asymptotic expansions in descending powers of √ κ are derived. The κ-independent coefficients of these expansions can be calculated in a simply way making these approximations quite useful in practise. An explicit error bound for the expansion of Mκ, μ(z) is also obtained.