T. M. Dunster

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

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 polynomials. The results are uniformly valid for $0\leq\mu\leq(1-\delta_0)\kappa<\kappa$, where $\delta_0\in(0,1)$ is arbitra...