Orthogonal Polynomials, Duality and Association Schemes

This paper reconstructs and characterizes the Askey–Wilson orthogonal polynomials as those having duals (in the sense of Delsarte) which are also orthogonal. It introduces the concepts of eigenvalues and Delsarte’s duality to the study of orthogonal polynomials and provides those interested in P- and Q-polynomial association schemes with a closed form for their parameters.