Dunkl-Xu polynomials with the weight (1-x^2-y^2)^β are written in terms of equal-parameter Jacobi polynomials. These can be generalized in two ways: with inequal-parameter Jacobi polynomials for a weight like (1-sqrt(x^2+y^2))^α(1+sqrt(x^2+y^2))^β; or with equal-parameter Jacobi polynomials with the quadratic transformations for a weight like (x^2+y^2)^α(1-x^2-y^2)^β. The latter, which I prefer due to their correspondence with generalized Zernike, are like 2D Konoplev OPs with a symmetric weight on [-1,1] with interior algebraic factor. @dlfivefifty
Dunkl-Xu polynomials with the weight
(1-x^2-y^2)^βare written in terms of equal-parameter Jacobi polynomials. These can be generalized in two ways: with inequal-parameter Jacobi polynomials for a weight like(1-sqrt(x^2+y^2))^α(1+sqrt(x^2+y^2))^β; or with equal-parameter Jacobi polynomials with the quadratic transformations for a weight like(x^2+y^2)^α(1-x^2-y^2)^β. The latter, which I prefer due to their correspondence with generalized Zernike, are like 2D Konoplev OPs with a symmetric weight on [-1,1] with interior algebraic factor. @dlfivefifty