The Jack polynomials are a family of multivariate orthogonal polynomials dependent on a positive parameter α. Orthogonality of the Jack polynomials is proved in Macdonald. The Jack polynomials have a rich history, and special cases of α have been studied more extensively than others . The following table summarizes some of these special cases. α | special polynomial 1/2 | quaternion zonal polynomial 1 | Schur polynomial 2 | zonal polynomial

zonal polynomial