Integral and series representations of the dirac delta function
Y. T. Li - Department of Mathematics, 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.
Received: April 2007; Revised: August 2007; Published: December 2007.
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