Orthogonal polynomials and hypergroups. II. The symmetric case

Abstract

The close relationship between orthogonal polynomial sequences and polynomial hypergroups is further studied in the case of even weight function, cf. [18]. Sufficient criteria for the recurrence relation of orthogonal polynomials are given such that a polynomial hypergroup structure is determined on N 0 {\mathbb {N}_0} . If the recurrence coefficients are convergent the dual spaces are determined explicitly. The polynomial hypergroup structure is revealed and investigated for associated ultraspherical polynomials, Pollaczek polynomials, associated Pollaczek polynomials, orthogonal polynomials with constant monic recursion formula and random walk polynomials.