We construct Jacobi-weighted orthogonal polynomials , on the triangular domain . We show that these polynomials over the triangular domain satisfy the following properties: , and for . And hence, , , form an orthogonal system over the triangular domain with respect to the Jacobi weight function. These Jacobi-weighted orthogonal polynomials on triangular domains are given in Bernstein basis form and thus preserve many properties of the Bernstein polynomial basis.
A. Rababah. M. Alqudah. "Jacobi-weighted orthogonal polynomials on triangular domains." J. Appl. Math. 2005 (3) 205 - 217, 30 June 2005. https://doi.org/10.1155/JAM.2005.205