Orthogonal polynomials on the real line generated by the parameter sequences for a given non-single parameter positive chain sequence

Abstract

In this paper, given a non-single parameter positive chain sequence ${\left\{d_{n+1}\right\}}_{n=1}^{\infty },$ we use all the non-minimal parameter sequences for ${\left\{d_{n+1}\right\}}_{n=1}^{\infty }$ in order to generate a whole family of sequences of orthogonal polynomials on the real line. For each non-minimal parameter sequence, the orthogonal polynomials and the associated orthogonality measure are obtained. As an application, corresponding quadratic decompositions are explicitly given. Some examples are considered in order to illustrate the results obtained.