Representations for the parameter derivatives of some Koornwinder polynomials

2015/06/17 by Rabia Aktas, Aktas, Rabia
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA

paper · pdf · doi:10.48550/arxiv.1506.05306

arxiv created 2016/02/28 · arxiv updated 2016/03/01

Abstract

In 1975, Koornwinder gave a method to construct orthogonal polynomials in two variables using the classical Jacobi polynomials. In [5], the authors introduced some new examples of Koornwinder polynomials obtained from the Koornwinder construction (see also [10]). The aim of this paper is to give the parameter derivative representations in the form of \frac∂ P_n,k(λ;x,y)∂λ = ∑_m=0^n-1 ∑_j=0^md_n,j,mP_m,j(λ;x,y) + ∑_j=0^ke_n,j,kP_n,j(λ;x,y) for some Koornwinder polynomials where λ is a parameter and 0≤ k≤ n; n,k=0,1,2,... and to present orthogonality properties of the parametric derivatives of these polynomials.

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