Recurrence relations for orthogonal polynomials on triangular domains (Q515427)

Summary: In Farouki et al. (2003), Legendre-weighted orthogonal polynomials \(\mathcal P_{n,r}(u,v,w)\), \(r=0,1,\dots,n\), \(n\geq 0\) on the triangular domain \(T=\{(u,v,w):u,v,w\geq 0,u+v+w=1\}\) are constructed, where \(u,v,w\) are the barycentric coordinates. Unfortunately, evaluating the explicit formulas requires many operations and is not very practical from an algorithmic point of view. Hence, there is a need for a more efficient alternative. A very convenient method for computing orthogonal polynomials is based on recurrence relations. Such recurrence relations are described in this paper for the triangular orthogonal polynomials, providing a simple and fast algorithm for their evaluation.