Orthogonal polynomials and operator orderings

Details Orthogonal polynomials and operator orderings Orthogonal polynomials and operator orderings

2010-06-04

arxiv.org/abs/1006.0808v1

JOURNAL OF MATHEMATICAL PHYSICS 51, 043506 (2010?)

Mathematics

Combinatorics

6 pages, 1 figure

Scientific paper

10.1063/1.3372526

An alternative and combinatorial proof is given for a connection between a system of Hahn polynomials and identities for symmetric elements in the Heisenberg algebra, which was first observed by Bender, Mead, and Pinsky [Phys. Rev. Lett. 56 (1986), J. Math. Phys. 28, 509 (1987)] and proved by Koornwinder [J. Phys. Phys. 30(4), 1989]. In the same vein two results announced by Bender and Dunne [J. Math. Phys. 29 (8), 1988] connecting a special one-parameter class of Hermitian operator orderings and the continuous Hahn polynomials are also proved.

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