On linearly related orthogonal polynomials and their functionals

[摘要] Let {P-n} be a sequence of polynomials orthogonal with respect a linear functional u and {Q(n)} a sequence of polynomials defined by P-n (x) + s(n) Pn-1 (x) = Q(n) (x) + t(n)Q(n-1) (x). We find necessary and sufficient conditions in order to {Q(n)} be a sequence of polynomials orthogonal with respect to a linear functional nu. Furthermore we prove that the relation between these linear functionals is (x - (a) over tilde )u = lambda(x - a)nu. Even more, if u and nu are linked in this way we get that {P-n} and {Q(n)} satisfy a formula as above. (C) 2003 Elsevier Inc. All rights reserved.

[发布日期] 2003-11-01

[关键词] orthogonal polynomials;recurrence relations;linear functionals