Results 31 to 40 of about 546 (189)
Journal of Mathematical Analysis and Applications, 2022 The purpose of this note is to characterize those orthogonal polynomials sequences $(P_n)_{n\geq0}$ for which $$ π(x)\mathcal{D}_q P_n(x)=(a_n x+b_n)P_n(x)+c_n P_{n-1}(x),\quad n=0,1,2,\dots, $$ where $\mathcal{D}_q$ is the Askey-Wilson operator, $π$ is a polynomial of degree at most 2, and $(a_n)_{n\geq0}$, $(b_n)_{n\geq0}$ and $(c_n)_{n\geq0}$ are ...
K. Castillo, D. Mbouna, J. Petronilho
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A new estimate for a quantity involving the Chebyshev polynomials of the first kind [PDF]
Journal of Mathematical Analysis and Applications, 2019 In this paper, we establish a new estimate (including lower and upper bounds) for an important quantity involved in the convergence analysis of smoothed aggregation algebraic multigrid methods. The new upper bound improves the existing ones. And our upper bound is optimal.
Xuefeng Xu, Chen-Song Zhang
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Complex Factorizations of the Lucas Sequences via Matrix Methods
Journal of Applied Mathematics, 2014 Firstly, we show a connection between the first Lucas sequence and the determinants of some tridiagonal matrices. Secondly, we derive the complex factorizations of the first Lucas sequence by computing those determinants with the help of Chebyshev ...
Honglin Wu
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Solving Non-Linear Fractional Variational Problems Using Jacobi Polynomials
Mathematics, 2019 The aim of this paper is to solve a class of non-linear fractional variational problems (NLFVPs) using the Ritz method and to perform a comparative study on the choice of different polynomials in the method.
Harendra Singh +2 more
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Some results on complex $(p,q)- $extnsion Chebyshev wavelets [PDF]
Journal of Mahani Mathematical ResearchIn this paper, we propose a generalized formula for well-known functions such as $(p,q)$-Chebyshev polynomials. Our consideration is focused on determining properties of generalized Chebyshev polynomials of the first and second kind, sparking interest ...
H. Mazaheri, A.W. Safi, S.M. Jesmani
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An Efficient Collocation Method for the Numerical Solutions of the Pantograph-Type Volterra Hammerstein Integral Equations and its Convergence Analysis [PDF]
Computational Algorithms and Numerical Dimensions, 2022 In this work, we consider a collocation method for solving the pantograph-type Volterra Hammerstein integral equations based on the first kind Chebyshev polynomials. We use the Lagrange interpolating polynomial to approximate the solution.
Hashem Saberi Najafi +2 more
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A characterization of ultraspherical, Hermite, and Chebyshev polynomials of the first kind [PDF]
Integral Transforms and Special Functions, 2016 We show that the only orthogonal polynomials with a generating function of the form $F(x z - αz^2)$ are the ultraspherical, Hermite, and Chebyshev polynomials of the first kind. For special $F$ for which this is the case, we then finish the classification of orthogonal polynomials with more general generating functions $F(x w(z) - R(z))$.
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Pseudo-Lucas Functions of Fractional Degree and Applications
Axioms, 2021 In a recent article, the first and second kinds of multivariate Chebyshev polynomials of fractional degree, and the relevant integral repesentations, have been studied. In this article, we introduce the first and second kinds of pseudo-Lucas functions of
Clemente Cesarano +2 more
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Fractal and Fractional, 2023 In this study, we present an innovative approach involving a spectral collocation algorithm to effectively obtain numerical solutions of the nonlinear time-fractional generalized Kawahara equation (NTFGKE).
Waleed Mohamed Abd-Elhameed +3 more
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Notes on explicit and inversion formulas for the Chebyshev polynomials of the first two kinds [PDF]
Miskolc Mathematical Notes, 2019 In the paper, starting from the Rodrigues formulas for the Chebyshev polynomials of the first and second kinds, by virtue of the Fa\`a di Bruno formula, with the help of two identities for the Bell polynomials of the second kind, and making use of a new inversion theorem for combinatorial coefficients, the authors derive two nice explicit formulas and ...
Qi, Feng, Niu, Da-Wei, Lim, Dongkyu
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