A special asymptotic limit of a Kampé de Fériet hypergeometric function appearing in nonhomogeneous Coulomb problems

In the investigation of two-body Coulomb Schrödinger equations with some types of nonhomogeneities, the particular solution can be expressed in terms of a two-variable Kampé de Fériet hypergeometric function. The asymptotic limit of the latter-for both variables being large but their ratio being a bound constant-is required in order to extract relevant physical information from the solutions. In this report the mathematical limit is provided. For that purpose, a particular series representation of the hypergeometric function-in terms of products of Kummer and Gauss functions-is first derived. © 2011 American Institute of Physics.Fil: Ancarani, L.U.. Université Paul Verlaine-Metz; FranciaFil: Gasaneo, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Sur. Departamento de Física; Argentin