American Institute of Mathematical Sciences

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March  2008, 7(2): 229-247. doi: 10.3934/cpaa.2008.7.229

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, Hong Kong
2. 

Liu Bie Ju Centre for Mathematical Sciences, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong

Received  April 2007 Revised  August 2007 Published  December 2007

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: Airy function, Coulomb wave function, spherical harmonics., Dirac delta function, Laguerre polynomials, Liouville-Green (WKB) approximation.
Mathematics Subject Classification: Primary: 46F99; Secondary: 33C10, 33C4.
Citation: Y. T. Li, R. Wong. Integral and series representations of the dirac delta function. Communications on Pure and Applied Analysis, 2008, 7 (2) : 229-247. doi: 10.3934/cpaa.2008.7.229
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