Biorthogonal expansion of non-symmetric Jack functions (Q2473512)

The Jack polynomials are known as a family of multivariate orthogonal polynomials that dependent on a positive parameters and the non-symmetric Jack polynomials occur as the polynomial part of the eigenfunctions of the Calogero-Sutherland model on a circle with exchange terms. In this study, the authors found a biorthogonal expansion of the Cayley transform of the non-symmetric Jack functions in terms of the non-symmetric Jack polynomials, the coefficients being Meixner-Pollaczek type polynomials by computing the Cherednik-Opdam transform of the non-symmetric Jack polynomials multiplied by the exponential function.