Representations for parameter derivatives of some Koornwinder polynomials in two variables

Author

Department of Mathematics, Ankara University, Ankara, Turkey

Abstract

In this paper, we give the parameter derivative representations in the form of
∂P n,k (λ; x, y )
∂λ
=
n −1
m =0
m
j=0
d n, j,m P m, j (λ; x, y ) +
k
j=0
e n, j,k P n, 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.

Keywords