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March 2005 Turán Inequalities and Zeros of Orthogonal Polynomials
Ilia Krasikov
Methods Appl. Anal. 12(1): 75-88 (March 2005).

Abstract

We use Turán type inequalities to give new non-asymptotic bounds on the extreme zeros of orthogonal polynomials in terms of the coefficients of their three term recurrence. Most of our results deal with symmetric polynomials satisfying the three term recurrence $p_{k+1}=x p_k-c_k p_{k-1},$ with a nondecreasing sequence $\{c_k\}$. As a special case they include a non-asymptotic version of Máté, Nevai and Totik result on the largest zeros of orthogonal polynomials with $c_k=c \; k^{2 \delta} (1+ o(k^{-2/3})).$ Our proof is based on new Turán inequalities which are obtained by analogy with higher order Laguerre inequalities.

Citation

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Ilia Krasikov. "Turán Inequalities and Zeros of Orthogonal Polynomials." Methods Appl. Anal. 12 (1) 75 - 88, March 2005.

Information

Published: March 2005
First available in Project Euclid: 6 June 2006

zbMATH: 1125.33006
MathSciNet: MR2203174

Rights: Copyright © 2005 International Press of Boston

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Vol.12 • No. 1 • March 2005
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