Author’s abstract: First, we discuss and correlate the various types of regularizations available in the literature for the singular function
is an integer and
is the Heaviside function. Then wepresent the corresponding regularization for the function
is the radial distance in
. Thereafter, we express the recently discovered distributional derivatives of this function in terms of pseudofunctional language commonly used in the Coulomb, gravitational, and interparticle potentials where the function
plays a fundamental role.