Generalized Gegenbauer orthogonal polynomials

[摘要] In this paper we explore a specific semi-classical orthogonal sequence, namely the generalized Gegenbauer orthogonal polynomials (GG) which appear in many applications such as the weighted L-p mean convergence of Hermite-Fejer interpolation or the chain of harmonic oscillators in the absence of externally applied forces. First we trace back the genesis of GG underlining its links with the Jacobi orthogonal polynomials. Second we establish a differential-difference relation and the second-order differential equation satisfied by this sequence. We end by giving the fourth-order differential equation satisfied by the association (of arbitrary order) of the GG. (C) 2001 Elsevier Science B.V. All rights reserved.

[发布日期] 2001-08-01

[效力级别]  Proceedings Paper

[关键词] orthogonal polynomials;second- and fourth-order differential equations;associated orthogonal polynomials;Gegenbauer polynomials