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Laguerre moments and generalized functions

Salomon S Mizrahi1 and Diógenes Galetti2

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Here we explore the link between the moments of the Laguerre polynomials or Laguerre moments and the generalized functions (as the Dirac delta-function and its derivatives), presenting several interesting relations. A useful application is related to a procedure for calculating mean values in quantum optics that makes use of the so-called quasi-probabilities. One of them, the P-distribution, can be represented by a sum over Laguerre moments when the electromagnetic field is in a photon-number state. Consequently, the P-distribution can be expressed in terms of Dirac delta-function and derivatives. More specifically, we found a direct relation between P-distributions and the Laguerre factorial moments.


PACS

02.30.Gp Special functions

42.50.Ar Photon statistics and coherence theory

02.10.De Algebraic structures and number theory

MSC

33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (See also 42C05 for general orthogonal polynomials and functions)

81V80 Quantum optics

Subjects

Mathematical physics

Optics, quantum optics and lasers

Dates

Issue 15 (19 April 2002)

Received 16 January 2002, in final form 15 February 2002

Published 5 April 2002



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