Results 1 to 10 of about 1,910 (137)
Representing Derivatives of Chebyshev Polynomials by Chebyshev Polynomials and Related Questions
Open Mathematics, 2017 A recursion formula for derivatives of Chebyshev polynomials is replaced by an explicit formula. Similar formulae are derived for scaled Fibonacci numbers.
Helmut Prodinger
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Some identities involving Chebyshev polynomials, Fibonacci polynomials and their derivatives [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 In this paper, we will derive the explicit formulae for Chebyshev polynomials of the third and fourth kind with odd and even indices using the combinatorial method. Similar results are also deduced for their rᵗʰ derivatives.
Jugal Kishore, Vipin Verma
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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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Chebyshev series: Derivation and evaluation
PLoS ONE, 2023 In this paper we use a contour integral method to derive a bilateral generating function in the form of a double series involving Chebyshev polynomials expressed in terms of the incomplete gamma function. Generating functions for the Chebyshev polynomial
Robert Reynolds, Allan Stauffer
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Advances in Difference Equations, 2021 The principal aim of the current article is to establish new formulas of Chebyshev polynomials of the sixth-kind. Two different approaches are followed to derive new connection formulas between these polynomials and some other orthogonal polynomials. The
Waleed M. Abd-Elhameed +1 more
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Fractal and Fractional, 2021 This paper is concerned with establishing novel expressions that express the derivative of any order of the orthogonal polynomials, namely, Chebyshev polynomials of the sixth kind in terms of Chebyshev polynomials themselves.
Waleed Mohamed Abd-Elhameed
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Проблемы анализа, 2020 In this paper, we give the generating functions of binary product between 2-orthogonal Chebyshev polynomials and kFibonacci, k-Pell, k-Jacobsthal numbers and the other orthogonal Chebyshev polynomials.
H. Merzouk, B. Aloui, A. Boussayoud
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Chebyshev Collocation Method for the Fractional Fredholm Integro-Differential Equations
Journal of New Theory, 2023 In this study, Chebyshev polynomials have been applied to construct an approximation method to attain the solutions of the linear fractional Fredholm integro-differential equations (IDEs).
Dilek Varol
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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 Applied Sciences and Environmental Management, 2006 In this paper, we proved the superiority of Legendre polynomial to Chebyshev polynomial in solving first order ordinary differential equation with rational coefficient.
FO Akinpelu, LA Adetunde, EO Omidiora
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