Integral and series representations of the Dirac delta function

Y. T. Li; R. Wong

doi:10.3934/cpaa.2008.7.229

Integral and series representations of the Dirac delta function

Y. T. Li
, R. Wong

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

20 Citations (Scopus)

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.

Original language	English
Pages (from-to)	229-247
Journal	Communications on Pure and Applied Analysis
Volume	7
Issue number	2
DOIs	https://doi.org/10.3934/cpaa.2008.7.229
Publication status	Published - Mar 2008

Research Keywords

Airy function
Coulomb wave function
Dirac delta function
Laguerre polynomials
Liouville-Green (WKB) approximation
Spherical harmonics

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AU - Li, Y. T.

AU - Wong, R.

PY - 2008/3

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N2 - 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.

AB - 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.

KW - Airy function

KW - Coulomb wave function

KW - Dirac delta function

KW - Laguerre polynomials

KW - Liouville-Green (WKB) approximation

KW - Spherical harmonics

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U2 - 10.3934/cpaa.2008.7.229

DO - 10.3934/cpaa.2008.7.229

M3 - RGC 21 - Publication in refereed journal

SN - 1534-0392

VL - 7

SP - 229

EP - 247

JO - Communications on Pure and Applied Analysis

JF - Communications on Pure and Applied Analysis

IS - 2

ER -

Integral and series representations of the Dirac delta function

Abstract

Research Keywords

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