scholarly journals Mehler–Heine formulas for orthogonal polynomials with respect to the modified Jacobi weight

2014 ◽  
Vol 142 (6) ◽  
pp. 2035-2045 ◽  
Author(s):  
Bujar Xh. Fejzullahu
Keyword(s):  
Orthogonal Polynomials ◽  
Jacobi Weight

scholarly journals Jacobi-weighted orthogonal polynomials on triangular domains

2005 ◽  
Vol 2005 (3) ◽  
pp. 205-217 ◽  
Author(s):  
A. Rababah ◽  
M. Alqudah
Keyword(s):  
Weight Function ◽  
Orthogonal Polynomials ◽  
Bernstein Polynomial ◽  
Orthogonal System ◽  
Polynomial Basis ◽  
Bernstein Basis ◽  
Triangular Domain ◽  
Jacobi Weight ◽  
Bernstein Polynomial Basis ◽  
Alpha Beta

We construct Jacobi-weighted orthogonal polynomials𝒫n,r(α,β,γ)(u,v,w),α,β,γ>−1,α+β+γ=0, on the triangular domainT. We show that these polynomials𝒫n,r(α,β,γ)(u,v,w)over the triangular domainTsatisfy the following properties:𝒫n,r(α,β,γ)(u,v,w)∈ℒn,n≥1,r=0,1,…,n,and𝒫n,r(α,β,γ)(u,v,w)⊥𝒫n,s(α,β,γ)(u,v,w)forr≠s. And hence,𝒫n,r(α,β,γ)(u,v,w),n=0,1,2,…,r=0,1,…,nform an orthogonal system over the triangular domainTwith 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.

scholarly journals Asymptotics of Sobolev orthogonal polynomials for a Jacobi weight

1997 ◽  
Vol 4 (4) ◽  
pp. 430-437
Author(s):  
Andrei Martínez-Finkelshtein ◽  
Juan J. Moreno-Balcázar
Keyword(s):  
Orthogonal Polynomials ◽  
Jacobi Weight ◽  
Sobolev Orthogonal Polynomials

scholarly journals ONSAGER'S ALGEBRA AND PARTIALLY ORTHOGONAL POLYNOMIALS

2002 ◽  
Vol 16 (14n15) ◽  
pp. 2129-2136 ◽  
Author(s):  
G. VON GEHLEN
Keyword(s):  
Weight Function ◽  
Orthogonal Polynomials ◽  
Potts Model ◽  
Jacobi Polynomials ◽  
Chiral Potts Model ◽  
Recursion Relations ◽  
Energy Eigenvalues ◽  
Special Polynomials ◽  
Jacobi Weight ◽  
Orthogonal Sequences

The energy eigenvalues of the superintegrable chiral Potts model are determined by the zeros of special polynomials which define finite representations of Onsager's algebra. The polynomials determining the low-sector eigenvalues have been given by Baxter in 1988. In the ℤ3-case they satisfy 4-term recursion relations and so cannot form orthogonal sequences. However, we show that they are closely related to Jacobi polynomials and satisfy a special "partial orthogonality" with respect to a Jacobi weight function.

On some properties of the orthogonal polynomials over a contour with general Jacobi weight

2016 ◽  
Vol 220 (5) ◽  
pp. 533-553
Author(s):  
Fahreddin G. Abdullayev ◽  
Gülnare A. Abdullayev
Keyword(s):  
Orthogonal Polynomials ◽  
Jacobi Weight
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