Orthogonal polynomials-centroid of their zeroes

Ronveaux, André
(2008) Numerical Algorithms — Vol. 49, n° 1-4, p. 373-385 (2008)

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  • Ronveaux, AndréUCLouvain
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Abstract
Let c (n,k) (k=1,...,n) the n zeroes of the monic orthogonal polynomials family P (n) (x). The centroid of these zeroes: 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 beta (n) , gamma (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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Ronveaux, A. (2008). Orthogonal polynomials-centroid of their zeroes. Numerical Algorithms, 49(1-4), 373-385. https://doi.org/10.1007/s11075-008-9195-6 (Original work published 2008)