Inequalities for Extreme Zeros of Some Classical Orthogonal and q-orthogonal Polynomials

K. Driver¹ ; K. Jordaan²

¹ Department of Mathematics and Applied Mathematics, University of Cape Town 7701, RSA
² Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, 0002, RSA

Mathematical modelling of natural phenomena, Tome 8 (2013) no. 1, pp. 48-59.

Résumé

Let {pn}∞n=0 be a sequence of orthogonal polynomials. We briefly review properties of pn that have been used to derive upper and lower bounds for the largest and smallest zero of pn. Bounds for the extreme zeros of Laguerre, Jacobi and Gegenbauer polynomials that have been obtained using different approaches are numerically compared and new bounds for extreme zeros of q-Laguerre and little q-Jacobi polynomials are proved.

Détail

DOI : 10.1051/mmnp/20138103

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