Results 21 to 30 of about 180,252 (161)
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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Two-dimensional limit series in ultraspherical Jacobi polynomials and their approximative properties [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. Информатика, 2021 Let $C[-1,1]$ be the space of functions continuous on the segment $[-1,1]$, $C[-1,1]^2$ be the space of functions continuous on the square $[-1,1]^2$. We denote by $P_n^\alpha(x)$ the ultraspherical Jacobi polynomials.
Guseinov, Ibraghim G. +1 more
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On the Direct Limit from Pseudo Jacobi Polynomials to Hermite Polynomials
Mathematics, 2021 In this short communication, we present a new limit relation that reduces pseudo-Jacobi polynomials directly to Hermite polynomials. The proof of this limit relation is based upon 2F1-type hypergeometric transformation formulas, which are applicable to ...
Elchin I. Jafarov +2 more
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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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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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Multivariate Jacobi and Laguerre polynomials, infinite-dimensional extensions, and their probabilistic connections with multivariate Hahn and Meixner polynomials [PDF]
, 2008 Multivariate versions of classical orthogonal polynomials such as Jacobi, Hahn, Laguerre, Meixner are reviewed and their connection explored by adopting a probabilistic approach.
Robert C. Griffiths +5 more
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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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