Further series expansions of the solutions of the confluent hypergeometric equation

Abstract

A convenient series expansion of the solutions of the confluent hypergeometric equation is developed for angular momentum quantum numbers l=2 and 3. Following a procedure proposed by Kuhn (1951) the expansion coefficients are deduced for the two independent solutions which may then be combined to give a series representation of the eigenfunctions. The results are couched in terms suitable for application to physical situations involving hydrogenic wavefunctions. The Coulomb (Whittaker) functions are written in terms of the Kuhn asymptotic series expansion with respect to a parameter related to the principal quantum number. The solutions are applied to find electron energy eigenvalues in the neighbourhood of a positive ion of finite size.