1993•Journal of Physics A Mathematical and GeneralOpen access

Generating function for the product of the associated Laguerre and Hermite polynomials

I. Mendaš

Abstract

The generating function for the product of the associated Laguerre and Hermite polynomials is formulated and used to determine the coordinate-space wave function of the displaced number states of the harmonic oscillator for the general case of a complex displacement parameter. The benefits, in this context, of an extended form of the associated Laguerre polynomials are advertised.

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Key concepts: Laguerre polynomials, Hermite polynomials, Laguerre's method, Classical orthogonal polynomials, Mathematics, Orthogonal polynomials, Context (archaeology), Product (mathematics)