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Title of Journal: Numer Algor

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Abbravation: Numerical Algorithms

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Springer US

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10.1007/978-1-4939-1453-1_13

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1572-9265

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Orthogonal polynomials—centroid of their zeroes

Authors: André Ronveaux
Publish Date: 2008/09/12
Volume: 49, Issue: 1-4, Pages: 373-385
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Abstract

Let c nk k=1n the n zeroes of the monic orthogonal polynomials family P n x The centroid of these zeroes s n=frac1n sumlimitsn k=1c nk controls globally the distribution of the zeroes and it is relatively easy to obtain information on s n like bounds inequalities parameters dependence from the links between s n the coefficients of the expansion of P n x and the coefficients β n γ n in the basic recurrence relation satisfied by P n x After a review of basic properties of the centroid on polynomials this work gives some results on the centroid of a large class of orthogonal polynomials

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