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 .
They generalize
Jack polynomials when the roots system is of type ''A'', and are limits of
Macdonald polynomials
In mathematics, Macdonald polynomials ''P''λ(''x''; ''t'',''q'') are a family of orthogonal symmetric polynomials in several variables, introduced by Macdonald in 1987. He later introduced a non-symmetric generalization in 1995. Macdonald origi ...
''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
[A new formula for weight multiplicities and characters, Theorem 1.3. about Heckman–Opdam polynomials, Siddhartha Sahi ]
References
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{{DEFAULTSORT:Heckman-Opdam polynomials
Orthogonal polynomials