Recurrence Relations for Jacobi Orthogonal Polynomials on the Triangular Domain

Authors

  • Wala’a A. AlKasasbeh
  • Abedallah Rababah
  • Iqbal M. Batiha Al Zaytoonah University of Jordan
  • Iqbal H. Jebril
  • Hamzah O. Al-Khawaldeh
  • Radwan M. Batyha

DOI:

https://doi.org/10.5566/ias.3603

Keywords:

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

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. 

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Published

2025-06-30 — Updated on 2025-07-01

Issue

Section

Original Research Paper

How to Cite

AlKasasbeh, W. A. ., Rababah, A. ., Batiha, I., Jebril, I. H., Al-Khawaldeh, H. O. ., & Batyha , R. M. (2025). Recurrence Relations for Jacobi Orthogonal Polynomials on the Triangular Domain. Image Analysis and Stereology, 44(2), 131-145. https://doi.org/10.5566/ias.3603

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