Heckman–Opdam polynomials
In mathematics, Heckman–Opdam polynomials (sometimes called Jacobi polynomials) Pλ(k) are orthogonal polynomials in several variables associated to root systems. They were introduced by Heckman and Opdam (1987).
They generalize Jack polynomials when the roots system is of type A, and are limits of Macdonald polynomials Pλ(q, t) as q tends to 1 and (1 − t)/(1 − q) tends to k.
References
- Heckman, G. J.; Opdam, E. M. (1987), "Root systems and hypergeometric functions. I", Compositio Math. 64 (3): 329–352, MR0918416, http://www.numdam.org/item?id=CM_1987__64_3_329_0
- Heckman, G. J.; Opdam, E. M. (1987b), "Root systems and hypergeometric functions. II", Compositio Math. 64 (3): 353–373, MR0918417, http://www.numdam.org/item?id=CM_1987__64_3_353_0
- Opdam, E. M. (1988), "Root systems and hypergeometric functions. III", Compositio Math. 67 (1): 21–49, MR0949270, http://www.numdam.org/item?id=CM_1988__67_1_21_0
- Opdam, E. M. (1988b), "Root systems and hypergeometric functions. IV", Compositio Math. 67 (2): 191–209., MR0951750, http://www.numdam.org/item?id=CM_1988__67_2_191_0