# Heckman–Opdam polynomials

In mathematics, **Heckman–Opdam polynomials** (sometimes called **Jacobi polynomials**) *P*_{λ}(*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 *P*_{λ}(*q*, *t*) as *q* tends to 1 and (1 − *t*)/(1 − *q*) tends to *k*.
Main properties of the Heckman–Opdam polynomials have been detailed by Siddhartha Sahi [1]

## References

- Heckman, G. J.; Opdam, E. M. (1987), "Root systems and hypergeometric functions. I",
*Compositio Mathematica*,**64**(3): 329–352, MR 0918416 - Heckman, G. J.; Opdam, E. M. (1987b), "Root systems and hypergeometric functions. II",
*Compositio Mathematica*,**64**(3): 353–373, MR 0918417 - Opdam, E. M. (1988), "Root systems and hypergeometric functions. III",
*Compositio Mathematica*,**67**(1): 21–49, MR 0949270 - Opdam, E. M. (1988b), "Root systems and hypergeometric functions. IV",
*Compositio Mathematica*,**67**(2): 191–209., MR 0951750

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