HYDROGENIC SLATER RADIAL INTEGRALS WITH DISCRETE PARAMETERS AND THEIR ASYMPTOTICS

Two-electronic matrix elements of the electrostatic interaction energy operator contain the hydrogenic radial integrals R_k(ab, cd) introduced by J.C. Slater. Their calculation and properties are widely used in the theory of atomic spectra. This paper deals with the study of these integrals by a new method, i.e. with the help of Appell hypergeometrical functions F₂(x, y) and their new properties. The exact analytical expressions for Slater radial integrals R_k, G_k, and F_k by means of Appell’s functions F₂(x, y) as well as the asymptotics of the general integral R_k, by one and two parameters in terms of Horn’s functions Ψ₁(x, y) are obtained.