Uniform asymptotic expansions for Whittaker's confluent hypergeometric functions

The asymptotic behavior, as $\kappa \to \infty $, of the Whittaker confluent hypergeometric functions $M_{\kappa ,\mu } (z)$ and $W_{\kappa ,\mu } (z)$ is examined. Asymptotic expansions are derived in terms of Bessel and Airy functions, the results being uniformly valid for real values of $\kappa $ and $\mu $ such that ${{0 \leqq \mu } / {\kappa \leqq A < 1}}$ (A an arbitrary constant), and for all complex values of the argument z. Explicit error bounds are available for all the approximations.