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Uniform asymptotic expansions are derived for Whittaker's confluenthypergeometric functions $M_{\kappa,\mu}(z)$ and $W_{\kappa,\mu}(z)$, as wellas the numerically satisfactory companion function $W_{-\kappa,\mu}(ze^{-\pii})$. The expansions are uniformly valid for $\mu \rightarrow \infty$, $0 \leq\kappa/\mu \leq 1-\delta <1$, and for $0 \leq \arg(z) \leq \pi$. By usingappropriate connection and analytic continuation formulas these expansions canbe extended to all unbounded nonzero complex $z$. The approximations come fromrecent asymptotic expansions involving elementary functions and Airy functions,and explicit error bounds are either provided or available.

Uniform asymptotic expansions for the Whittaker functions $M_{\kappa,\mu}(z)$ and $W_{\kappa,\mu}(z)$ with $\mu$ large