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Zbl 1132.33315
Koornwinder, Tom H.
Lowering and raising operators for some special orthogonal polynomials. (English)
[A] Kuznetsov, Vadim B. (ed.) et al., Jack, Hall-Littlewood and Macdonald polynomials. Workshop on Jack, Hall-Littlewood and Macdonald polynomials, ICMS, Edinburgh, UK, September 23--26, 2003. Providence, RI: American Mathematical Society (AMS). Contemporary Mathematics 417, 227-238 (2006). ISBN 0-8218-3683-8/pbk

Summary: This paper discusses operators lowering or raising the degree but preserving the parameters of special orthogonal polynomials. Results for one-variable classical ($q$-)orthogonal polynomials are surveyed. For Jacobi polynomials associated with root system $BC_2$ a new pair of lowering and raising operators is obtained.

MSC 2000:: *33C45 Orthogonal polynomials and functions of hypergeometric type
33D45 Basic hypergeometric functions and integrals in several variables
33C52 Orthogonal polynomials and functions associated with root systems
05E35 Orthogonal polynomials (combinatorics)

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