Generalized Tschebyscheff-II weighted polynomials on simplicial domain

Abstract

In this paper, we construct generalized Tschebyscheff-type weighted orthogonal polynomials Un,r(γ,M,N)(u,v,w), γ > −1, in the Bernstein-Bézer form over the simplicial domain. We show that Un,r(γ,M,N)(u,v,w), r = 0,1,...,n; n=0,1,2,..., form an orthogonal system over a triangular domain with respect to the generalized weight function.