Results 11 to 20 of about 6,252 (234)
On the Generalized Class of Multivariable Humbert-Type Polynomials
International Journal of Mathematics and Mathematical SciencesThe present paper deals with the class of multivariable Humbert polynomials having generalization of some well-known polynomials like Gegenbauer, Legendre, Chebyshev, Gould, Sinha, Milovanović-Djordjević, Horadam, Horadam-Pethe, Pathan and Khan, a class ...
B. B. Jaimini +3 more
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On the L 2 -norm of Gegenbauer polynomials. [PDF]
Math Sci (Karaj), 2022 AbstractGegenbauer, also known as ultra-spherical, polynomials appear often in numerical analysis or interpolation. In the present text we find a recursive formula for and compute the asymptotic behavior of their $$L^2$$ L 2 -norm.
Ferizović D.
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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^{(λ)}(x))^2(1-x)^α(1+x)^β\, dx, \end{equation*} where $C_n^{(λ)}$ denotes the Gegenbauer-polynomial of index $λ>0$ and $α,β>-1$. 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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Analytic Univalent fucntions defined by Gegenbauer polynomials [PDF]
Journal of Mahani Mathematical Research, 2023 The numerical tools that have outshinning many others in the history of Geometric Function Theory (GFT) are the Chebyshev and Gegenbauer polynomials in the present time.
Sunday Olatunji
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Universal Journal of Mathematics and Mathematical Sciences, 2021 Summary: In this paper, it is shown that the terms of Gegenbauer polynomial satisfy the Jacobi identity.
U. E. Edeke, N. E. Udo
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Fourier Series of Gegenbauer-Sobolev Polynomials [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2018 We study the partial sum operator for a Sobolev-type inner product related to the classical Gegenbauer polynomials. A complete characterization of the partial sum operator in an appropriate Sobolev space is given. Moreover, we analyze the convergence of the partial sum operators.
Universidad de La Rioja, Spain +3 more
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A Rodrigues-type formula for Gegenbauer matrix polynomials
Applied Mathematics Letters, 2013 Emilio Defez
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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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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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Applied Mathematics in Science and Engineering, 2022 In recent years, using the idea of analytic and bi-univalent functions, many ideas have been developed by different well-known authors, but the using Gegenbauer polynomials along with certain bi-univalent functions is very rare in the literature.
Qiuxia Hu +5 more
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