Let {P n } be a sequence of polynomials orthogonal with respect a linear functional u and {Q n } a sequence of polynomials defined byWe find necessary and sufficient conditions in order to {Q n } 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 −ã)u = λ(x − a)v. Even more, if u and v are linked in this way we get that {P n } and {Q n } satisfy a formula as above.
Let u be a quasi-definite linear functional. We find necessary and sufficient conditions in order to the linear functional v satisfying (x −ã)u = λ(x − a)v be a quasi-definite one. Also we analyze some linear relations linking the polynomials orthogonal with respect to u and v.
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