Asymptotic expansions of the Whittaker functions for large order parameter (Q1582296)

In this paper the asymptotic expansion of the Whittaker function \(M_{\kappa, \mu}(z)\) for bounded values of \(z\neq 0\) and \(\mu\) and large values of \(\kappa\) in inverse powers of \(\sqrt\kappa\) is derived. An estimate of the remainder is given too. The expansion is not uniform, but it is useful for applications, since the coefficients of the expansion can be calculated in a simple way.