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_nQ_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.