Recurrence Relations for Jacobi Orthogonal Polynomials on the Triangular Domain
DOI:
https://doi.org/10.5566/ias.3603Keywords:
Bernstein polynomials, Jacobi polynomials, orthogonal polynomials, recurrence relations, triangular domainsAbstract
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.
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Copyright (c) 2025 Wala’a A. AlKasasbeh, Abedallah Rababah, Iqbal M. Batiha, Iqbal H. Jebril, Hamzah O. Al-Khawaldeh, Radwan M. Batyha

This work is licensed under a Creative Commons Attribution 4.0 International License.