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Representations for the extreme zeros of orthogonal polynomials

By Erik A. van Doorn, Nicky D. van Foreest and Alexander I. Zeifman

Abstract

AbstractWe establish some representations for the smallest and largest zeros of orthogonal polynomials in terms of the parameters in the three-terms recurrence relation. As a corollary we obtain representations for the endpoints of the true interval of orthogonality. Implications of these results for the decay parameter of a birth–death process (with killing) are displayed

Publisher: Elsevier B.V.
Year: 2009
DOI identifier: 10.1016/j.cam.2009.02.051
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