Representations for parameter derivatives of some Koornwinder polynomials in two variables

Author

Department of Mathematics, Ankara University, Ankara, Turkey

10.1016/j.joems.2016.01.004

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