𝒫n,r(α,β,γ)(u,v,w),α,β,γ>−1,α+β+γ=0, on the triangular domain T. We show that these polynomials 𝒫n,r(α,β,γ)(u,v,w) over the triangular domain T satisfy the following properties: 𝒫n,r(α,β,γ)(u,v,w)∈ℒn,n≥1, r=0,1,…,n, and 𝒫n,r(α,β,γ)(u,v,w)⊥𝒫n,s(α,β,γ)(u,v,w) for r≠s. And hence, 𝒫n,r(α,β,γ)(u,v,w), n=0,1,2,…, r=0,1,…,n form an orthogonal system over the triangular domain T with respect to the Jacobi weight function. These Jacobi-weighted orthogonal polynomials on triangular domains are given in Bernstein basis form and thus preserve many properties of the Bernstein polynomial basis."> Jacobi-weighted orthogonal polynomials on triangular domains - raybet雷竞app,雷竞技官网下载,雷电竞下载苹果
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Volume 2005 |Article ID 478261 | https://doi.org/10.1155/JAM.2005.205

A. Rababah, M. Alqudah, "Jacobi-weighted orthogonal polynomials on triangular domains",Journal of Applied Mathematics, vol.2005, Article ID478261, 13 pages, 2005. https://doi.org/10.1155/JAM.2005.205

Jacobi-weighted orthogonal polynomials on triangular domains

A. Rababah1and M. Alqudah1

1Department of Mathematics and Statistics, Jordan University of Science and Technology, Jordan

Received 25 Mar 2004
Revised 20 Mar 2005

Abstract

We construct Jacobi-weighted orthogonal polynomials n , r ( α , β , γ ) ( u , v , w ) , α , β , γ > − 1 , α + β + γ = 0 , on the triangular domain T . We show that these polynomials n , r ( α , β , γ ) ( u , v , w ) over the triangular domain T satisfy the following properties: n , r ( α , β , γ ) ( u , v , w ) ∈ ℒ n , n ≥ 1 , r = 0 , 1 , … , n , and n , r ( α , β , γ ) ( u , v , w ) ⊥ n , s ( α , β , γ ) ( u , v , w ) for r ≠ s . And hence, n , r ( α , β , γ ) ( u , v , w ) , n = 0 , 1 , 2 , … , r = 0 , 1 , … , n form an orthogonal system over the triangular domain T with respect to the Jacobi weight function. These Jacobi-weighted orthogonal polynomials on triangular domains are given in Bernstein basis form and thus preserve many properties of the Bernstein polynomial basis.

Copyright © 2005 Hindawi Publishing Corporation. This is an open access article distributed under theCreative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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