Bivariate Chebyshev-I Weighted Orthogonal Polynomials on Simplicial Domains

Abstract

We construct a simple closed-form representation of degree-ordered system of bivariate Chebyshev-I orthogonal polynomials ${\mathcal{T}}_{n,r}(u,v,w)$ on simplicial domains. We show that these polynomials ${\mathcal{T}}_{n,r}(u,v,w),$ $r=0,1,\dots ,n;$ $n\ge 0$ form an orthogonal system with respect to the Chebyshev-I weight function.