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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 J Duran
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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.
Paul Névai, Tamás Erdelyi
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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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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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Jacobi's Generating Function for Jacobi Polynomials [PDF]
Proceedings of the American Mathematical Society, 1978 An idea of Hermite is used to give a simple proof of Jacobi’s generating function for Jacobi polynomials.
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On the Approximation of the Jacobi Polynomials
Rocky Mountain Journal of Mathematics, 2007 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Elias, Uri, Gingold, Harry
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Jacobi Polynomials on the Bernstein Ellipse [PDF]
Journal of Scientific Computing, 2017 In this paper, we are concerned with Jacobi polynomials $P_n^{(α,β)}(x)$ on the Bernstein ellipse with motivation mainly coming from recent studies of convergence rate of spectral interpolation. An explicit representation of $P_n^{(α,β)}(x)$ is derived in the variable of parametrization. This formula further allows us to show that the maximum value of $
Haiyong Wang, Lun Zhang
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Bispectral Jacobi type polynomials [PDF]
Advances in Applied Mathematics, 2022 23 pages.
Antonio J. Durán +1 more
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On the denseness of Jacobi polynomials [PDF]
International Journal of Mathematics and Mathematical Sciences, 2004 Let X represent either a space C[−1, 1] or , 1 ≤ p < ∞, of functions on [−1, 1]. It is well known that X are Banach spaces under the sup and the p‐norms, respectively. We prove that there exist the best possible normalized Banach subspaces of X such that the system of Jacobi polynomials is densely spread on these, or, in other words, each can be ...
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