Integral and Series Representations of the Dirac Delta Function

2013/03/08 by Y. T. Li, R. Wong · 1 citation
Mathematics · #math.CA #msc:46F99 #msc:33C10 #msc:33C45

paper · pdf · doi:10.3934/cpaa.2008.7.229

published as Communications on Pure and Applied Analysis, 7 (2008), 229-247 · 19 pages, 1 figure

arxiv created 2013/03/08 · arxiv updated 2013/03/11

Abstract

Mathematical justifications are given for several integral and series representations of the Dirac delta function which appear in the physics literature. These include integrals of products of Airy functions, and of Coulomb wave functions; they also include series of products of Laguerre polynomials and of spherical harmonics. The methods used are essentially based on the asymptotic behavior of these special functions.

Cited by

• Dirac delta function [wikipedia]

Related

• On regularizations of the integral representation of Dirac delta function -- elementary approach
• Identities for number series and their reciprocals: Dirac delta function approach
• The complex Dirac Delta, Plemelj formula, and integral representations
• A Cauchy-Dirac delta function
• On Dirac's Delta Calculus