First, we discuss and correlate the various types of regularizations available in the literature for the singular function H(x) xk, 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 Rn. 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. © 1989.
Publication Source (Journal or Book title)
Journal of Mathematical Analysis and Applications
Estrada, R., & Kanwal, R. (1989). Regularization, pseudofunction, and hadamard finite part. Journal of Mathematical Analysis and Applications, 141 (1), 195-207. https://doi.org/10.1016/0022-247X(89)90216-3