Generalized second-order partial derivatives of 1/r

Abstract: The generalized second-order partial derivatives of 1/r, where r is the radial distance in 3D, are obtained using a result of the potential theory of classical analysis. Some non-spherical regularization alternatives to the standard spherical-regularization expression for the derivatives are derived. The utility of a spheroidal-regularization expression is illustrated on an example from classical electrodynamics.