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Lowering and raising operators for some special orthogonal polynomials. (English) Zbl 1132.33315
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) (ISBN 0-8218-3683-8/pbk). Contemporary Mathematics 417, 227-238 (2006).
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:
33C45Orthogonal polynomials and functions of hypergeometric type
33D45Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)
33C52Orthogonal polynomials and functions associated with root systems
05E35Orthogonal polynomials (combinatorics) (MSC2000)