RECURRENCE RELATIONS FOR JACOBI WEIGHTED ORTHOGONAL POLYNOMIALS ON THE TRIANGULAR DOMAIN

Wala'a A. Alkasasbeh; Abedallah Rababah; Iqbal M. Batiha; Iqbal H. Jebril; Hamzah O. Al-Khawaldeh; Radwan M. Batyha

doi:10.5566/ias.3603

RECURRENCE RELATIONS FOR JACOBI WEIGHTED ORTHOGONAL POLYNOMIALS ON THE TRIANGULAR DOMAIN

Wala'a A. Alkasasbeh
, Abedallah Rababah
, Iqbal M. Batiha
, Iqbal H. Jebril
, Hamzah O. Al-Khawaldeh
, Radwan M. Batyha

Al-Zaytoonah University of Jordan
United Arab Emirates University
Al al-Bayt University
Applied Science Private University

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we present recurrence relations for the Jacobi weighted orthogonal polynomials P_n,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.

Original language	English
Pages (from-to)	131-145
Number of pages	15
Journal	Image Analysis and Stereology
Volume	44
Issue number	2
DOIs	https://doi.org/10.5566/ias.3603
State	Published - 2025
Externally published	Yes

Keywords

Bernstein polynomials
Jacobi polynomials
orthogonal polynomials
recurrence relations
triangular domains.

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10.5566/ias.3603

Cite this

@article{14daf1aabaec4cf7a67d571ba2e2d074,

title = "RECURRENCE RELATIONS FOR JACOBI WEIGHTED 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.",

author = "Alkasasbeh, \{Wala'a A.\} and Abedallah Rababah and Batiha, \{Iqbal M.\} and Jebril, \{Iqbal H.\} and Al-Khawaldeh, \{Hamzah O.\} and Batyha, \{Radwan M.\}",

year = "2025",

doi = "10.5566/ias.3603",

language = "English",

volume = "44",

pages = "131--145",

journal = "Image Analysis and Stereology",

issn = "1580-3139",

publisher = "Slovenian Society For Stereology And Quantitative Image Analysis",

number = "2",

}

TY - JOUR

T1 - RECURRENCE RELATIONS FOR JACOBI WEIGHTED ORTHOGONAL POLYNOMIALS ON THE TRIANGULAR DOMAIN

AU - Alkasasbeh, Wala'a A.

AU - Rababah, Abedallah

AU - Batiha, Iqbal M.

AU - Jebril, Iqbal H.

AU - Al-Khawaldeh, Hamzah O.

AU - Batyha, Radwan M.

PY - 2025

Y1 - 2025

N2 - 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.

AB - 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.

KW - Bernstein polynomials

KW - Jacobi polynomials

KW - orthogonal polynomials

KW - recurrence relations

KW - triangular domains.

UR - https://www.scopus.com/pages/publications/105010944446

U2 - 10.5566/ias.3603

DO - 10.5566/ias.3603

M3 - Article

AN - SCOPUS:105010944446

SN - 1580-3139

VL - 44

SP - 131

EP - 145

JO - Image Analysis and Stereology

JF - Image Analysis and Stereology

IS - 2

ER -

RECURRENCE RELATIONS FOR JACOBI WEIGHTED ORTHOGONAL POLYNOMIALS ON THE TRIANGULAR DOMAIN

Abstract

Keywords

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