Results 31 to 40 of about 110,049 (182)
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^{(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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Matrix-Valued Gegenbauer-Type Polynomials [PDF]
Constructive Approximation, 2017 Introducimos funciones de peso con valor de matriz de tamaño arbitrario, que son análogas a la función de peso para Gegenbauer o polinomios ultraesféricos para el parámetro $$\nu >0$$ . La descomposición LDU del peso se da explícitamente en términos de polinomios de Gegenbauer.
Erik Koelink +2 more
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An Operational Matrix Method Based on the Gegenbauer Polynomials for Solving a Class of Fractional Optimal Control Problems [PDF]
International Journal of Industrial Electronics, Control and Optimization, 2021 One of the most important classes of fractional calculus is the fractional optimal control problem (FOCP), which arises in engineering. This study presents a direct and efficient numerical method for solving a class of (FOCPs) in which the fractional ...
Farzaneh Soufivand +2 more
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Some relations on Humbert matrix polynomials [PDF]
Mathematica Bohemica, 2016 The Humbert matrix polynomials were first studied by Khammash and Shehata (2012). Our goal is to derive some of their basic relations involving the Humbert matrix polynomials and then study several generating matrix functions, hypergeometric matrix ...
Ayman Shehata
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Some results for sums of products of Chebyshev and Legendre polynomials
Advances in Difference Equations, 2019 In this paper, we perform a further investigation of the Gegenbauer polynomials, the Chebyshev polynomials of the first and second kinds and the Legendre polynomials.
Yuan He
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Advances in Difference Equations, 2019 In this paper, we investigate sums of finite products of Chebyshev polynomials of the first kind and those of Lucas polynomials. We express each of them as linear combinations of Hermite, extended Laguerre, Legendre, Gegenbauer, and Jacobi polynomials ...
Taekyun Kim +3 more
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Quasilinearization method to solve several classes of nonlinear Lane-Emden equations by Gegenbauer polynomials [PDF]
Iranian Journal of Numerical Analysis and OptimizationThis paper presents a comprehensive numerical approach for solving various types of singular nonlinear Lane-Emden equations. The proposed method begins by applying the Quasilinearization Method (QLM), to transform the nonlinear differential equation into
Fateme Sheikhi, Bahman Ghazanfari
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Mathematics, 2018 This paper is concerned with representing sums of the finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials in terms of several classical orthogonal polynomials.
Taekyun Kim +3 more
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Bilinear and Bilateral generating functions for the Gegenbauer Polynomials [PDF]
, 2018 Bu çalışma Gegenbauer (veya ultraküresel) polinomları için bilineer ve bilateral doğurucu fonksiyonlarla ilgilidir. Gegenbauer polinomları için bazı özel durumları, çeşitli özelliklerini, multilinear ve multilateral doğurucu fonksiyonları elde ...
Özmen, Nejla
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