Jack polynomial

In mathematics, the Jack function is a generalization of the Jack polynomial, introduced by Henry Jack. The Jack polynomial is a homogeneous, symmetric polynomial which generalizes the Schur and zonal polynomials, and is in turn generalized by the Heckman–Opdam polynomials and Macdonald polynomials.

The Jack function ${\displaystyle J_{\kappa }^{(\alpha )}(x_{1},x_{2},\ldots )}$ of integer partition ${\displaystyle \kappa }$, parameter ${\displaystyle \alpha }$, and indefinitely many arguments ${\displaystyle x_{1},x_{2},\ldots ,}$ can be recursively defined as follows:

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