Recurrence Relations for Jacobi Orthogonal Polynomials on the Triangular Domain
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 univari...
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| Format: | Article |
| Language: | English |
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Slovenian Society for Stereology and Quantitative Image Analysis
2025-07-01
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| Series: | Image Analysis and Stereology |
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| Online Access: | https://www.ias-iss.org/ojs/IAS/article/view/3603 |
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| author | Wala’a A. AlKasasbeh Abedallah Rababah Iqbal Batiha Iqbal H. Jebril Hamzah O. Al-Khawaldeh Radwan M. Batyha |
| author_facet | Wala’a A. AlKasasbeh Abedallah Rababah Iqbal Batiha Iqbal H. Jebril Hamzah O. Al-Khawaldeh Radwan M. Batyha |
| author_sort | Wala’a A. AlKasasbeh |
| collection | DOAJ |
| description |
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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| format | Article |
| id | doaj-art-8dff8038a2d24fca86b2579e1e1306c6 |
| institution | Kabale University |
| issn | 1580-3139 1854-5165 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | Slovenian Society for Stereology and Quantitative Image Analysis |
| record_format | Article |
| series | Image Analysis and Stereology |
| spelling | doaj-art-8dff8038a2d24fca86b2579e1e1306c62025-08-20T03:29:34ZengSlovenian Society for Stereology and Quantitative Image AnalysisImage Analysis and Stereology1580-31391854-51652025-07-0144210.5566/ias.3603Recurrence Relations for Jacobi Orthogonal Polynomials on the Triangular DomainWala’a A. AlKasasbehAbedallah RababahIqbal Batiha0Iqbal H. JebrilHamzah O. Al-KhawaldehRadwan M. Batyha Al Zaytoonah University of Jordan 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. https://www.ias-iss.org/ojs/IAS/article/view/3603Bernstein polynomialsJacobi polynomialsorthogonal polynomialsrecurrence relationstriangular domains |
| spellingShingle | Wala’a A. AlKasasbeh Abedallah Rababah Iqbal Batiha Iqbal H. Jebril Hamzah O. Al-Khawaldeh Radwan M. Batyha Recurrence Relations for Jacobi Orthogonal Polynomials on the Triangular Domain Image Analysis and Stereology Bernstein polynomials Jacobi polynomials orthogonal polynomials recurrence relations triangular domains |
| title | Recurrence Relations for Jacobi Orthogonal Polynomials on the Triangular Domain |
| title_full | Recurrence Relations for Jacobi Orthogonal Polynomials on the Triangular Domain |
| title_fullStr | Recurrence Relations for Jacobi Orthogonal Polynomials on the Triangular Domain |
| title_full_unstemmed | Recurrence Relations for Jacobi Orthogonal Polynomials on the Triangular Domain |
| title_short | Recurrence Relations for Jacobi Orthogonal Polynomials on the Triangular Domain |
| title_sort | recurrence relations for jacobi orthogonal polynomials on the triangular domain |
| topic | Bernstein polynomials Jacobi polynomials orthogonal polynomials recurrence relations triangular domains |
| url | https://www.ias-iss.org/ojs/IAS/article/view/3603 |
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