Quasi-orthogonality with applications to some families of classical orthogonal polynomials

Authors:
C. Brezinski;K. A. Driver;M. Redivo-Zaglia
Affiliations:
Laboratoire de Mathématiques Appliquées, FRE CNRS 2222, UFR de Mathématiques Pures et Appliquées, Université des Sciences et Technologies de Lille, 59655 Villeneuve d'Ascq ...;School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, South Africa;Università degli Studi di Padova, Dipartimento di Matematica Pura ed Applicata, Via G.B. Belzoni 7, 35131 Padova, Italy
Venue:
Applied Numerical Mathematics
Year:
2004

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Abstract

In this paper, we study the quasi-orthogonality of orthogonal polynomials. New results on the location of their zeros are given in two particular cases. Then these results are applied to Gegenbauer, Jacobi and Laguerre polynomials when the restrictions on the parameters involved in their definitions are not satisfied. The corresponding weight functions are investigated and the location of their zeros is discussed.