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Representations for the extreme zeros of orthogonal polynomials

✍ Scribed by Erik A. van Doorn; Nicky D. van Foreest; Alexander I. Zeifman

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
378 KB
Volume
233
Category
Article
ISSN
0377-0427

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✦ Synopsis

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.

πŸ“œ SIMILAR VOLUMES

Zeros of orthogonal polynomials on the r
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✍ Sergey A Denisov; Barry Simon πŸ“‚ Article πŸ“… 2003 πŸ› Elsevier Science 🌐 English βš– 144 KB

Let p n Γ°xÞ be the orthonormal polynomials associated to a measure dm of compact support in R: If EesuppΓ°dmÞ; we show there is a d40 so that for all n; either p n or p nΓΎ1 has no zeros in Γ°E Γ€ d; E ΓΎ dÞ: If E is an isolated point of suppΓ°mÞ; we show there is a d so that for all n; either p n or p nΓΎ