Results 21 to 30 of about 4,491 (232)

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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On integer Chebyshev polynomials [PDF]

Mathematics of Computation, 1997
We are concerned with the problem of minimizing the supremum norm on [ 0 , 1 ] \lbrack 0,1\rbrack of a nonzero polynomial of degree at most n n with integer coefficients. We use the structure of such polynomials to derive an efficient algorithm for computing them.
Laurent Habsieger, Bruno Salvy
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Numerical Treatment of Multi-Term Fractional Differential Equations via New Kind of Generalized Chebyshev Polynomials

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, Muhammad Mahmoud Alsuyuti   +1 more
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Generalizations of Chebyshev polynomials and polynomial mappings [PDF]

Transactions of the American Mathematical Society, 2007
In this paper we show how polynomial mappings of degree K \mathfrak {K} from a union of disjoint intervals onto [ − 1 , 1 ] [-1,1] generate a countable number of special cases of generalizations of Chebyshev polynomials.
Yang Chen, James Griffin, James Griffin, Mourad E. H. Ismail   +3 more
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An extension of the Chebyshev polynomials

Journal of Computational and Applied Mathematics, 2005
Let \(U_{n}(q;\,e^{i\theta})\) be the polynomials defined by the generating function \[ \frac{1}{(1-ze^{i\theta})(1-qze^{-i\theta})}=\sum_{n=0}^{\infty}U_{n}(q;\,e^{i\theta})z^{n}, \] where \(z\) belongs to the unit disc \(\mathbb{D}\), \(-\pi\leq \theta \leq \pi ...
Katarzyna Kiepiela, Dominika Klimek
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A property of Chebyshev polynomials [PDF]

Journal of Approximation Theory, 1974
THEOREM. rf P is a polynomial of degree n with n distinct zeros in [ 1, l] and 1 P(cos(k+z)/ = 1, k = 0, l,..., n, (1) then either P(x) = m(x) or P(x) = -T,(x), where T,(x) = cos(n arc cos x) is the Chebyshev polynomial of degree n. This theorem answers affirmatively a problem posed by C. Micchelli and T.
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On Chebyshev polynomials and their applications [PDF]

Advances in Difference Equations, 2017
Abstract The main purpose of this paper is, using some properties of the Chebyshev polynomials, to study the power sum problems for the sinx and cosx functions and to obtain some interesting computational formulas.
Xingxing Lv, Shimeng Shen
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Superiority of legendre polynomials to Chebyshev polynomial in solving ordinary differential equation

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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Coefficient bounds for certain subclasses of bi-prestarlike functions associated with the Chebyshev polynomials [PDF]

Mathematica Moravica, 2020
In this paper, we introduce and investigate a new subclass of bi-prestarlike functions defined in the open unit disk, associated with Chebyshev Polynomials.
Güney H.Ö., Murugusundaramoorthy G., Vijaya K., Thilagavathi K.   +3 more
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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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