New recurrence relations for Wilson polynomials via a system of Jacobi type orthogonal functions

Abstract

In this paper, we will find an orthogonal basis in term of explicit Jacobi polynomials, of the corresponding weighted L2-space on the whole of the real numbers, which is mapped onto another orthogonal basis involving Wilson polynomials by the Jacobi-Dunkl transform. Next we give a tridiagonalization of the Jacobi-Dunkl Laplacian for the Jacobi type functions. This tridiagonalization leads to a new result, which can be viewed as contiguous relations for Wilson polynomials.