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 (-)orthogonal polynomials are surveyed. For Jacobi polynomials associated with root system a new pair of lowering and raising operators is obtained.
|33C45||Orthogonal polynomials and functions of hypergeometric type|
|33D45||Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)|
|33C52||Orthogonal polynomials and functions associated with root systems|
|05E35||Orthogonal polynomials (combinatorics) (MSC2000)|