On linearly related orthogonal polynomials and their functionals

Let {Pn} be a sequence of polynomials orthogonal with respect a linear functional u and {Qn} a sequence of polynomials defined by Pn(x) + snPn−1(x) =Qn(x) + tnQn−1(x). We find necessary and sufficient conditions in order to {Qn} be a sequence of polynomials orthogonal with respect to a linear functional v. Furthermore we prove that the relation between these linear functionals is (x − ˜a)u = λ(x − a)v. Even more, if u and v are linked in this way we get that {Pn} and {Qn} satisfy a formula as above.  2003 Elsevier Inc. All rights reserved