Recurrence Relations for Jacobi Orthogonal Polynomials on the Triangular Domain - Wala’a A. AlKasasbeh; Abedallah Rababah; Iqbal Batiha; Iqbal H. Jebril; Hamzah O. Al-Khawaldeh; Radwan M. Batyha (Image Analysis and Stereology, 2025)
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.