Creation and Annihilation Operators for Orthogonal Polynomials of Continuous and Discrete Variables

2004/01/06 by M. Lorente
Physics and Astronomy · Mathematics · #math-ph #math.MP

paper · pdf

published as El. Trans. Num. Anal. 9 (1999) 102-111 · LaTeX, 9 pages, uses siamltex.sty (late submission)

arxiv created 2004/01/06 · arxiv updated 2009/12/01

Abstract

We develop general expressions for the raising and lowering operators that belong to the orthogonal polynomials of hypergeometric type with discrete and continuous variable. We construct the creation and annihilation operators that correspond to the normalized polynomials and study their algebraic properties in the case of the Kravchuk/Hermite Meixner/Laguerre polynomials.

Related

• Systems of orthogonal polynomials defined by hypergeometric type equations
• The annihilation operator for certain family of q-Hermite Sobolev-type orthogonal polynomials
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• Laguerre-Freud Equations for the Generalized Charlier, Generalized Meixner and Gauss Hypergeometric Orthogonal Polynomials