Integral and series representations of the dirac delta function

Y. T. Li; R. Wong

doi:10.3934/cpaa.2008.7.229

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2008, Volume 7, Issue 2: 229-247. Doi: 10.3934/cpaa.2008.7.229

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Integral and series representations of the dirac delta function

Y. T. Li^1, and
R. Wong^2,

1.
Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon
2.
Liu Bie Ju Centre for Mathematical Sciences, City University of Hong Kong, Tat Chee Avenue, Kowloon

Received: March 31, 2007

Revised: July 31, 2007

Published: February 2008

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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.

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Mathematics Subject Classification: Primary: 46F99; Secondary: 33C10, 33C45.

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