Derivatives of a finite class of orthogonal polynomials defined on the positive real line related to F-distribution

Abstract

Among the six classes of classical orthogonal polynomials, three of them are infinite, namely Jacobi, Hermite and Laguerre and the remaining three are finite and characterized by Masjed Jamei (2002) [5]. In this work, we consider derivatives of one such finite class of orthogonal polynomials that are orthogonal with respect to the weight function which is related to the probability density function of the F distribution. For this derivative class, besides orthogonality we find various other related properties such as the normal form and the self adjoint form. The corresponding Gaussian quadrature formulae are also given. Examples are provided to support the advantages of considering this derivative class of the finite class of orthogonal polynomials. © 2010 Elsevier Ltd. All rights reserved.