2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58466We consider one-dimensional regularizations of the Coulomb potential formed by taking a two-dimensional expectation of the Coulomb potential with respect to the Landau states. It is well-known that such functions arises naturally in the study of atoms in strong magnetic fields. For many-electron atoms consideration of the Pauli principle requires convex combinations of such potentials and interactions in which the regularizations also contain a 2^{-1/2} rescaling. We summarize the results of a comprehensive study of these functions including recursion relations, tight bounds, convexity properties, and connections with confluent hypergeometric functions. We also report briefly on their application in one-dimensional models of many-electrons atoms in strong magnetic fields.9 pages, Proceedings of a conference on Differential Equations and Mathematical Physics at University of Alabama Birmingham (March 1998)Mathematical PhysicsClassical Analysis and ODEsAtomic Physics81V45, 33E20text