Representations for parameter derivatives of some Koornwinder polynomials in two variables

In this paper, we give the parameter derivative representations in the form of ∂Pn,k(λ;x,y)∂λ=∑m=0n−1∑j=0mdn,j,mPm,j(λ;x,y)+∑j=0ken,j,kPn,j(λ;x,y)for some Koornwinder polynomials where λ is a parameter and 0 ≤ k ≤ n; n=0,1,2,… and present orthogonality properties of the parametric derivatives of these polynomials.