Recurrence Relations for Jacobi Orthogonal Polynomials on the Triangular Domain

Abstract

In this paper, we present recurrence relations for the Jacobi weighted orthogonal polynomials Pn,r(α,β,γ) (u, v, w) with r = 0, 1, . . . , n, where n ≥ 0, defined on the triangular domain T = {(u, v, w) : u, v, w ≥ 0, u + v + w = 1} for values of α, β, γ > −1. In particular, we construct univariate recurrence relations for Jacobi polynomials when w = 0, considering three specific cases. These recurrence relations provide an efficient and straightforward alternative for computing Jacobi polynomials, offering a simpler approach compared to traditional methods.

Keywords

• Bernstein polynomials
• Jacobi polynomials
• orthogonal polynomials
• recurrence relations
• triangular domains