Jacobi‐weighted orthogonal polynomials on triangular domains

A. Rababah and M. Alqudah

Journal of Applied Mathematics, 2005, vol. 2005, issue 3, 205-217

Abstract: We construct Jacobi‐weighted orthogonal polynomials 𝒫n,r(α,β,γ)(u,v,w),α,β,γ>−10,α+β+γ=, 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.

Date: 2005
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https://doi.org/10.1155/JAM.2005.205

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2005:y:2005:i:3:p:205-217

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