Representations for the extreme zeros of orthogonal polynomials

Authors:
Erik A. van Doorn;Nicky D. van Foreest;Alexander I. Zeifman
Affiliations:
Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands;Faculty of Management and Organization, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands;Vologda State Pedagogical University and Vologda Scientific Coordinate Centre of CEMI RAS, S. Orlova 6, Vologda, Russia
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Erratum: Corrigendum to "Representations for the extreme zeros of orthogonal polynomials" [J. Comput. Appl. Math. 233 (2009) 847-851]

Journal of Computational and Applied Mathematics

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Abstract

We 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.