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Fourier, Gegenbauer and Jacobi Expansions for a Power-Law Fundamental Solution of the Polyharmonic Equation and Polyspherical Addition Theorems [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2013 We develop complex Jacobi, Gegenbauer and Chebyshev polynomial expansions for the kernels associated with power-law fundamental solutions of the polyharmonic equation on d-dimensional Euclidean space.
Howard S. Cohl
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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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Enhancing low-light images using Sakaguchi type function and Gegenbauer polynomial [PDF]
Scientific ReportsEnhancing low-light images is crucial for various applications in computer vision, yet current approaches often fall short in balancing image quality and detail preservation.
K. Sivagami Sundari, B. Srutha Keerthi
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Journal of High Energy Physics, 2022 We investigate radiatively stable classes of pseudo-Nambu-Goldstone boson (pNGB) potentials for approximate spontaneously broken SO(N + 1) → SO(N). Using both the one-loop effective action and symmetry, it is shown that a Gegenbauer polynomial potential ...
Gauthier Durieux +2 more
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Matrix-Valued Gegenbauer-Type Polynomials [PDF]
Constructive Approximation, 2017 Matrix-valued Gegenbauer-type polynomials are investigated. The main results of the paper are stated in Sections 2 and 3. In Section 2 the matrix-valued weight functions \(W^{(\nu)}(x)\), which are analogues of the weight function for the Gegenbauer polynomials \(C^{(\nu)}_n(x)\) are introduced: \(W^{(\nu)}(x)= (1-x^2)^{\nu-1/2}W^{(\nu)}_{\mathrm{pol}}(
Koelink, Erik +2 more
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Journal of Nigerian Society of Physical Sciences, 2023 In this paper, approximation of space fractional order diffusion equation are considered using compact finite difference technique to discretize the time derivative, which was then approximated via shifted Gegenbauer polynomials using zeros of (N - 1 ...
Kazeem Issa +3 more
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Weighted $$L^2$$-norms of Gegenbauer polynomials [PDF]
Aequationes mathematicae, 2022 We study integrals of the form \begin{equation*} \int_{-1}^1(C_n^{( )}(x))^2(1-x)^ (1+x)^ \, dx, \end{equation*} where $C_n^{( )}$ denotes the Gegenbauer-polynomial of index $ >0$ and $ , >-1$. We give exact formulas for the integrals and their generating functions, and obtain asymptotic formulas as $n\to\infty$.
Johann S. Brauchart, Peter J. Grabner
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Lietuvos Matematikos Rinkinys, 2021 The article investigates the properties of two alternative disaggregation methods. First one, proposed in Chong (2006), is based on the assumption of polynomial autoregressive parameter density. Second one, proposed in Leipus et al.
Dmitrij Celov +2 more
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A NEW CHARACTERIZATION OF SYMMETRIC DUNKL AND \(q\)-DUNKL-CLASSICAL ORTHOGONAL POLYNOMIALS
Ural Mathematical Journal, 2023 In this paper, we consider the following \(\mathcal{L}\)-difference equation $$\Phi(x) \mathcal{L}P_{n+1}(x)=(\xi_nx+\vartheta_n)P_{n+1}(x)+\lambda_nP_{n}(x),\quad n\geq0,$$where \(\Phi\) is a monic polynomial (even), \(\deg\Phi\leq2\), \(\xi_n ...
Yahia Habbachi
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Alexandria Engineering Journal, 2021 In this paper, a new type of wavelet method to solve fractional differential equations (linear or nonlinear) is proposed. The proposed method is based on the generalized Gegenbauer–Humbert polynomial.
Jumana H.S. Alkhalissi +4 more
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