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 \begin{ equation*} \frac{ \partial P_{ n,k}(\lambda;x,y)}{ \partial\lambda} = \sum_{ m=0}^{ n-1} \sum_{ j=0}^{ m}d_{ n,j,m}P_{ m,j}(\lambda;x,y) + \sum_{ j=0}^{ k}e_{ n,j,k}P_{ n,j}(\lambda;x,y) \end{ equation*} for some Koornwinder polynomials where $\lambda$ is a parameter and $0\leq k\leq n$; $n,k=0,1,2,...$ and to present orthogonality properties of the parametric derivatives of these polynomials.
Categories: math.CA