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Representations for the extreme zeros of orthogonal polynomials |
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| Authors: | Erik A van Doorn Nicky D van Foreest |
| Institution: | a Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands b Faculty of Management and Organization, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands c Vologda State Pedagogical University and Vologda Scientific Coordinate Centre of CEMI RAS, S. Orlova 6, Vologda, Russia |
| 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. |
| Keywords: | primary 42C05 secondary 60J80 |
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