Application of the discrete classical case to a 1−2 type relation

Abstract

In this paper, we present a simple approach in order to build up recursively the connection coefficients between a sequence of polynomials {Q n } n≥0 and an orthogonal polynomials sequence {P n } n≥0 when P n (x) = Q n (x) +r n Q n −1 (x), n≥0. This yields the relation between the parameters of the corresponding recurrence relations. Some special cases are developed. More specifically, assuming that {P n } n≥0 is a discrete classical orthogonal polynomials sequence.