Whittaker functions with one or both parameters large: simplified uniform asymptotic expansions involving Bessel and Airy functions

T. M. Dunster

Uniform asymptotic expansions are derived as $\kappa \to \infty$ for the Whittaker functions $W_{\kappa ,\mu }(z)$, $M_{\kappa ,\mu }(z)$, as well as related functions including generalized Laguerre polyn…