Abstract
In this paper we study orthogonal polynomials ( p n ) which arise from a given system of orthogonal polynomials ( p n ) by a finite perturbation of the recurrence coefficients, i.e., the recurrence coefficients ( α n ), ( λ n + 1 ) of ( p n ) respectively (α n ), (λ n + 1 ) of ( p n ) are related to each other by α n + l = α n + m and λ n + 1 + l = λ n + 1 + m for Nϵ N , where l and m are fixed nonnegative integers. Closed expressions for the polynomial p n in terms of p n and its associated polynomial p n − 1 (1) as well as for the orthogonality measure μ of ( p n ) in terms of the orthogonality measure μ of ( p n ) are given. In fact the results are presented for the most general case when μ is an arbitrary, not necessarily positive, measure.
Published Version
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