Turan inequalities and zeros of orthogonal polynomials

Details Turan inequalities and zeros of orthogonal polynomials Turan inequalities and zeros of orthogonal polynomials

2004-01-22

arxiv.org/abs/math/0401299v1

Mathematics

Classical Analysis and ODEs

Scientific paper

We use Turan 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 Mate, Nevai and Totik result on the largest zeros of orthogonal polynomials with $c_k=k^{\delta} (1+ o(k^{-2/3})).$

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