The Whittaker function \(M_{\kappa,\mu}\) as a function of \(\kappa\)
The well-known Whittaker function \(M_{\kappa ,\mu }(z)\) for the value of the parameter \(\kappa =c/z\) is closely related to the Coulombian solution of the Schrödinger equation. The authors give a convergent series for \(M_{\kappa ,\mu }(z)\) in ascending powers of \(\kappa \) and its asymptotic expansion in descending powers of \(\kappa \). The coefficients of the first expansion are analyzed in both the cases of small and large values of \(| z| \).
scientific article; zbMATH DE number 1271884