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Zbl 0672.33011
Koornwinder, Tom H.
(Sharapudinov, I.I.)
Meixner-Pollaczek polynomials and the Heisenberg algebra. (English)
[J] J. Math. Phys. 30, No.4, 767-769 (1989). ISSN 0022-2488; ISSN 1089-7658/e

Bender, Mead and Pinsky found a very interesting representation for a number of terms containing n factors of each of p and q when $[p,q]=i$. The representation is in terms of some symmetric continuous Hahn polynomials, or equivalently, for some symmetric Meixner-Pollaczek polynomials. Their proof was sketchy. Details are provided. Some very interesting operational formulas are derived along the way.
[R.Askey]

MSC 2000:: *33C45 Orthogonal polynomials and functions of hypergeometric type
33C80 Connections of theory of special functions with groups and algebras
81S05 Commutation relations (quantum theory)

Keywords: Heisenberg algebra; Hahn polynomials; Meixner-Pollaczek polynomials

Cited in: Zbl 1023.81015 Zbl 0868.33011

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