Results 1 to 10 of about 109 (104)
Jaynes-Gibbs Entropic Convex Duals and Orthogonal Polynomials [PDF]
Entropy, 2022 The univariate noncentral distributions can be derived by multiplying their central distributions with translation factors. When constructed in terms of translated uniform distributions on unit radius hyperspheres, these translation factors become ...
Richard Le Blanc
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Uniform pointwise estimates for ultraspherical polynomials [PDF]
Comptes Rendus. Mathématique, 2022 We prove pointwise bounds for two-parameter families of Jacobi polynomials. Our bounds imply estimates for a class of functions arising from the spectral analysis of distinguished Laplacians and sub-Laplacians on the unit sphere in arbitrary dimension ...
Casarino, Valentina +2 more
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Determinant inequalities for sieved ultraspherical polynomials [PDF]
International Journal of Mathematics and Mathematical Sciences, 2001 Paul Turan first observed that the Legendre polynomials satisfy the inequality Pn2(x)−Pn−1(x)Pn(x)>0 ...
J. Bustoz, I. S. Pyung
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An identity for ultraspherical polynomials
Journal of Numerical Analysis and Approximation Theory, 1995 Not available.
Luciana Lupaş
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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 ...
Arvesú, J. +2 more
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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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Sieved Ultraspherical Polynomials [PDF]
Transactions of the American Mathematical Society, 1984 The continuous q q -ultraspherical polynomials contain a number of important examples as limiting or special cases. One of these arose in Allaway’s Ph.D. thesis. In a previous paper we solved a characterization problem essentially equivalent to Allaway’s and showed that these polynomials arose from the q q ...
Al-Salam, Waleed +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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A modeling method for vibration analysis of cracked beam with arbitrary boundary condition
Journal of Ocean Engineering and Science, 2018 This paper establishes a cracked Timoshenko beams model to investigate the vibration behavior based on the ultraspherical polynomials. Timoshenko beam theory is applied to model the free vibration analysis of the cracked beam and the numerical results ...
Kwanghun Kim +4 more
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Fractal and Fractional, 2021 Herein, we developed and analyzed a new fractal–fractional (FF) operational matrix for orthonormal normalized ultraspherical polynomials. We used this matrix to handle the FF Riccati differential equation with the new generalized Caputo FF derivative ...
Youssri Hassan Youssri
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