Lowering and raising operators for some special orthogonal polynomials
arXiv:math/0505378
Abstract
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.
12 pages; to appear in proceedings of the Workshop on Jack, Hall-Littlewood and Macdonald polynomials (Edinburgh, September 2003)