ON CONNECTING WEYL-ORBIT FUNCTIONS TO JACOBI POLYNOMIALS AND MULTIVARIATE (ANTI)SYMMETRIC TRIGONOMETRIC FUNCTIONS

Abstract

The aim of this paper is to make an explicit link between the Weyl-orbit functions and the corresponding polynomials, on the one hand, and to several other families of special functions and orthogonal polynomials on the other. The cornerstone is the connection that is made between the one-variable orbit functions of A1 and the four kinds of Chebyshev polynomials. It is shown that there exists a similar connection for the two-variable orbit functions of A2 and a specific version of two variable Jacobi polynomials. The connection with recently studied G2-polynomials is established. Formulas for connection between the four types of orbit functions of Bn or Cn and the (anti)symmetric multivariate cosine and sine functions are explicitly derived.