Results 21 to 30 of about 122,453 (243)
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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Inequalities for Jacobi polynomials [PDF]
The Ramanujan Journal, 2013 A Bernstein type inequality is obtained for the Jacobi polynomials $P_n^{ , }(x)$, which is uniform for all degrees $n\ge0$, all real $ , \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 ...
Haagerup, Uffe, Schlichtkrull, Henrik
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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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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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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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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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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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Bispectral Jacobi type polynomials [PDF]
Advances in Applied Mathematics, 2022 23 pages.
Antonio J. Durán +1 more
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Iterated Integrals of Jacobi Polynomials [PDF]
Bulletin of the Malaysian Mathematical Sciences Society, 2019 Let P(α,β)n be the n-th monic Jacobi polynomial with α,β>−1. Given m numbers ω1,…,ωm∈C∖[−1,1], let Ωm=(ω1,…,ωm) and P(α,β)n,m,Ωm be the m-th iterated integral of (n+m)!n!P(α,β)n normalized by the conditions dkP(α,β)n,m,Ωmdzk(ωm−k)=0, for k=0,1,…,m−1. The main purpose of the paper is to study the algebraic and asymptotic properties of the sequence of ...
Hector Pijeira-Cabrera +1 more
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Parameter Derivatives of the Jacobi Polynomials with Three Variables on the Simplex
MATEC Web of Conferences, 2016 In this paper, an attempt has been made to derive parameter derivatives of Jacobi polynomials with three variables on the simplex. They are obtained via parameter derivatives of the classical Jacobi polynomials Pn(α,β)(x) with respect to their parameters.
Aktaş Rabia
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