Cubature formula for bivariate generalized Chebyshev Koornwinder's type polynomials

摘要

We formulate an explicit form of degree-ordered system of bivariate generalized Chebyshev Koornwinder's type polynomials U_(n,r,d)~(γ,M,N)(u,v,w)(γ > -1 in Bezer form over a triangular domain T. These polynomials form an orthogonal system with respect to the generalized measure 2/π(1-x~2)~(1/2)+Mδ_(-1)+Nδ_1 where M, N ≥ 0 and δ_x is a singular Dirac measure. Then, we study cu-bature formulas to approximate double integrals for bivariate generalized Chebyshev Koornwinder's type polynomials, U_(n,r,d)~(γ,M,N)(U) over T.