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.

12 pages; as accepted for publication by European Journal of Physics

References in corpus (1)

• Regularization of the second-order partial derivatives of the Coulomb potential of a point charge

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