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30 June 2005 Jacobi-weighted orthogonal polynomials on triangular domains
A. Rababah, M. Alqudah
J. Appl. Math. 2005(3): 205-217 (30 June 2005). DOI: 10.1155/JAM.2005.205


We construct Jacobi-weighted orthogonal polynomials 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)n,n1, r=0,1,,n, and 𝒫n,r(α,β,γ)(u,v,w)𝒫n,s(α,β,γ)(u,v,w) for rs. 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.


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A. Rababah. M. Alqudah. "Jacobi-weighted orthogonal polynomials on triangular domains." J. Appl. Math. 2005 (3) 205 - 217, 30 June 2005.


Published: 30 June 2005
First available in Project Euclid: 25 July 2005

zbMATH: 1095.33005
MathSciNet: MR2201971
Digital Object Identifier: 10.1155/JAM.2005.205

Rights: Copyright © 2005 Hindawi


Vol.2005 • No. 3 • 30 June 2005
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