Abstract

First, we discuss and correlate the various types of regularizations available in the literature for the singular function H(x)/x^k, where k is an integer and H(x) is the Heaviside function. Then we present the corresponding regularization for the function r^−k, where r is the radial distance in _n. 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 1/r plays a fundamental role.

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