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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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Mixed-Type Hypergeometric Bernoulli–Gegenbauer Polynomials
Mathematics, 2023 In this paper, we consider a novel family of the mixed-type hypergeometric Bernoulli–Gegenbauer polynomials. This family represents a fascinating fusion between two distinct categories of special functions: hypergeometric Bernoulli polynomials and ...
Dionisio Peralta +2 more
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Some identities involving generalized Gegenbauer polynomials [PDF]
Advances in Difference Equations, 2017 In this paper, we investigate some interesting identities on the Bernoulli, Euler, Hermite and generalized Gegenbauer polynomials arising from the orthogonality of generalized Gegenbauer polynomials in the generalized inner product 〈 p 1 ( x ) , p 2 ( x )
Zhaoxiang Zhang
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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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A NEW EXTENSIONS OF GEGENBAUER POLYNOMIALS
مجلّة جامعة عدن للعلوم الأساسيّة والتّطبيقيّة, 2020 The main aim of this paper is to introduce new extensions of Gegenbauer polynomials of one and two variables by using the extended Gamma function given by Chaudhry and Zubair [3]. Some properties of these extended polynomials such as generating functions,
Ahmed Ali Atash, Ahmed Ali Al-Gonah
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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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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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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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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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