Results 11 to 20 of about 13,679 (194)
Fractal and Fractional, 2023 The main aim of this paper is to introduce a new class of orthogonal polynomials that generalizes the class of Chebyshev polynomials of the first kind. Some basic properties of the generalized Chebyshev polynomials and their shifted ones are established.
Waleed Mohamed Abd-Elhameed +1 more
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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 $$ (x)\mathcal{D}_q P_n(x)=(a_n x+b_n)P_n(x)+c_n P_{n-1}(x),\quad n=0,1,2,\dots, $$ where $\mathcal{D}_q$ is the Askey-Wilson operator, $ $ 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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Spectral Treatment of High-Order Emden–Fowler Equations Based on Modified Chebyshev Polynomials
Axioms, 2023 This paper is devoted to proposing numerical algorithms based on the use of the tau and collocation procedures, two widely used spectral approaches for the numerical treatment of the initial high-order linear and non-linear equations of the singular type,
Waleed Mohamed Abd-Elhameed +3 more
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Chebyshev Polynomials and Spectral Method for Optimal Control Problem [PDF]
Engineering and Technology Journal, 2009 This paper presents efficient algorithms which are based on applying the idea of spectral method using the Chebyshev polynomials: including Chebyshev polynomials of the first kind, Chebyshev polynomials of the second kind and shifted Chebyshev ...
Suha Najeeb Shihab, Jabbar Abed Eleiwy
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Some Identities Involving the Derivative of the First Kind Chebyshev Polynomials [PDF]
Mathematical Problems in Engineering, 2015 We use the combinatorial method and algebraic manipulations to obtain several interesting identities involving the power sums of the derivative of the first kind Chebyshev polynomials. This solved an open problem proposed by Li (2015).
Wang, Tingting, Zhang, Han
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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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Powers Sums of the First and Second Kinds of Chebyshev Polynomials
Iranian Journal of Science and Technology, Transactions A: Science, 2020 Odd powers of even-indexed Chebyshev polynomials of the second kind and odd powers of odd-indexed Chebyshev polynomials of the first kind were computed. In this paper, we evaluate all of the rest kinds of power sums of the Chebyshev polynomials. We present the relationships between the Chebyshev polynomials and general Fibonacci, Lucas sequences.
Kılıç, Emrah +2 more
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A new class of orthogonal polynomials for solving logarithmic singular integral equations
Ain Shams Engineering Journal, 2020 In this note, we propose a new class of orthogonal polynomials (named Bachok–Hasham polynomials H1nk(x)), which is an extension of the Chebyshev polynomials.
H. Alhawamda +3 more
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The Chebyshev Difference Equation
Mathematics, 2020 We define and investigate a new class of difference equations related to the classical Chebyshev differential equations of the first and second kind.
Tom Cuchta +2 more
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Limit theorems for linear eigenvalue statistics of overlapping matrices [PDF]
, 2015 The paper proves several limit theorems for linear eigenvalue statistics of overlapping Wigner and sample covariance matrices. It is shown that the covariance of the limiting multivariate Gaussian distribution is diagonalized by choosing the Chebyshev ...
Kargin, Vladislav
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