Generalized Gegenbauer orthogonal polynomials
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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 Lp mean convergence of Hermite–Fejér 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.
论文关键词:primary 33C45,33D45,42C05,34-XX,secondary 34Kxx,39A10,Orthogonal polynomials,Second- and fourth-order differential equations,Associated orthogonal polynomials,Gegenbauer polynomials
论文评审过程:Received 29 October 1999, Revised 28 January 2000, Available online 3 August 2001.
论文官网地址:https://doi.org/10.1016/S0377-0427(00)00643-9