Jacobi-weighted orthogonal polynomials on triangular domains

A. Rababah and M. Alqudah

Journal of Applied Mathematics, 2005, vol. 2005, 1-13

Abstract:

We construct Jacobi-weighted orthogonal polynomials 𝒫 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 𝒫 n , r ( α , β , γ ) ( u , v , w ) over the triangular domain T satisfy the following properties: 𝒫 n , r ( α , β , γ ) ( u , v , w ) ∈ ℒ n , n ≥ 1 , r = 0 , 1 , … , n , and 𝒫 n , r ( α , β , γ ) ( u , v , w ) ⊥ 𝒫 n , s ( α , β , γ ) ( u , v , w ) for r ≠ s . And hence, 𝒫 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.

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:478261

DOI: 10.1155/JAM.2005.205

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