Integral and series representations of the dirac delta function

Pages: 229 - 247, Volume 7, Issue 2, March 2008      doi:10.3934/cpaa.2008.7.229

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Y. T. Li - Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong (email)
R. Wong - Liu Bie Ju Centre for Mathematical Sciences, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong (email)

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.

Keywords:  Dirac delta function, Liouville-Green (WKB) approximation, Airy function, Coulomb wave function, Laguerre polynomials, spherical harmonics.
Mathematics Subject Classification:  Primary: 46F99; Secondary: 33C10, 33C45.

Received: April 2007;      Revised: August 2007;      Available Online: December 2007.