Extension and Simple Proof of Lekner's Summation Formula for Coulomb Forces

Abstract

Abstract In [3] J. Lekner derived an elegant and very useful summation formula for Coulomb forces. In his derivation he used some powerful identities such as the Poisson-Jacobi identity, the application of which was not at all straightforward. In this note it is shown that Lekner's result and an extension to more general potentials can be obtained in a rather simple and straightforward way.