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Representation of ( p , q ) $(p,q)$ -Bernstein polynomials in terms of ( p , q ) $(p,q)$ -Jacobi polynomials [PDF]
Journal of Inequalities and Applications, 2017 A representation of ( p , q ) $(p,q)$ -Bernstein polynomials in terms of ( p , q ) $(p,q)$ -Jacobi polynomials is obtained.
F Soleyman +3 more
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Exceptional Jacobi polynomials [PDF]
Journal of Approximation Theory, 2019 40 pages, 1 ...
Niels Bonneux
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Exceptional Jacobi polynomials which are deformations of Jacobi polynomials
Journal of Mathematical Analysis and Applications, 2023 Exceptional polynomials are complete orthogonal polynomial systems with respect to a positive measure in the real line which in addition are eigenfunctions of a second order differential operator. The most apparent difference between classical orthogonal polynomials and their exceptional counterparts is that the exceptional families have gaps in their ...
Antonio José Durán Guardeño
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New Formulae for the High-Order Derivatives of Some Jacobi Polynomials: An Application to Some High-Order Boundary Value Problems [PDF]
The Scientific World Journal, 2014 This paper is concerned with deriving some new formulae expressing explicitly the high-order derivatives of Jacobi polynomials whose parameters difference is one or two of any degree and of any order in terms of their corresponding Jacobi polynomials ...
W. M. Abd-Elhameed
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Generalized Jacobi Weights, Christoffel Functions, and Jacobi Polynomials [PDF]
SIAM Journal on Mathematical Analysis, 1994 Let \(\omega(x)= (1- x)^ \alpha(1+ x)^ \beta\), \(\alpha>-1\), \(\beta>- 1\), \(x\in [-1,1]\), and let \(\{p_ n(\omega,x)\}\) be the set of Jacobi polynomials which are orthogonal with respect to \(\omega(x)\) over \([- 1,1]\). With a view to determining the constant involved in the known inequality (\textit{L. Gatteschi} [SIAM J. Math. Anal.
Tamás Erdelyi +2 more
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On linearization coefficients of Jacobi polynomials
Applied Mathematics Letters, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hamza Chaggara, Wolfram Koepf
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Mathematics, 2021 This article deals with the general linearization problem of Jacobi polynomials. We provide two approaches for finding closed analytical forms of the linearization coefficients of these polynomials.
Waleed Mohamed Abd-Elhameed +1 more
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Beta Jacobi Ensembles and Associated Jacobi Polynomials [PDF]
Journal of Statistical Physics, 2021 Beta ensembles on the real line with three classical weights (Gaussian, Laguerre and Jacobi) are now realized as the eigenvalues of certain tridiagonal random matrices. The paper deals with beta Jacobi ensembles, the type with the Jacobi weight. Making use of the random matrix model, we show that in the regime where $βN \to const \in [0, \infty)$, with
Hoang Dung Trinh, Khanh Duy Trinh
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Reproducing kernel method for solving partial two-dimensional nonlinear fractional Volterra integral equation [PDF]
Journal of Mahani Mathematical Research, 2023 This article discusses the replicating kernel interpolation collocation method related to Jacobi polynomials to solve a class of fractional system of equations. The reproducing kernel function that is executed as an (RKM) was first created in the form of
Reza Alizadeh +3 more
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An algebraic treatment of the Askey biorthogonal polynomials on the unit circle
Forum of Mathematics, Sigma, 2021 A joint algebraic interpretation of the biorthogonal Askey polynomials on the unit circle and of the orthogonal Jacobi polynomials is offered. It ties their bispectral properties to an algebra called the meta-Jacobi algebra $m\mathfrak {J}$ .
Luc Vinet, Alexei Zhedanov
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