Results 11 to 20 of about 2,335 (226)
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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Zeros of Jacobi and ultraspherical polynomials [PDF]
The Ramanujan Journal, 2021 Suppose $\{P_{n}^{(α, β)}(x)\}_{n=0}^\infty $ is a sequence of Jacobi polynomials with $ α, β>-1.$ We discuss special cases of a question raised by Alan Sokal at OPSFA in 2019, namely, whether the zeros of $ P_{n}^{(α,β)}(x)$ and $ P_{n+k}^{(α+ t, β+ s )}(x)$ are interlacing if $s,t >0$ and $ k \in \mathbb{N}.$ We consider two cases of this ...
J. Arvesú +2 more
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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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Inequalities for Jacobi polynomials [PDF]
The Ramanujan Journal, 2013 A Bernstein type inequality is obtained for the Jacobi polynomials $P_n^{α,β}(x)$, which is uniform for all degrees $n\ge0$, all real $α,β\ge0$, and all values $x\in [-1,1]$. It provides uniform bounds on a complete set of matrix coefficients for the irreducible representations of $\mathrm{SU}(2)$ with a decay of $d^{-1/4}$ in the dimension $d$ of the ...
Haagerup, Uffe, Schlichtkrull, Henrik
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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 $ N \to const \in [0, \infty ...
Hoang Dung Trinh, Khanh Duy Trinh
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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. 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 Approximation of the Jacobi Polynomials [PDF]
Rocky Mountain Journal of Mathematics, 2007 New approximations of the Jacobi polynomials P (α,β) n (x) are provided on the interval (1,∞). The approximations are given explicitly in terms of some expressions derived from a coefficient of a related hypergeometric equation and in terms of certain perturbation terms.
Elias, Uri, Gingold, Harry
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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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RECURRENCE RELATIONS FOR SOBOLEV ORTHOGONAL POLYNOMIALS
Проблемы анализа, 2020 We consider recurrence relations for the polynomials orthonormal with respect to the Sobolev-type inner product and generated by classical orthogonal polynomials, namely: Jacobi polynomials, Legendre polynomials, Chebyshev polynomials of the first and ...
M. S. Sultanakhmedov
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