  We 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.
