Results 1 to 10 of about 31,852 (174)
Optimization via Chebyshev Polynomials [PDF]
Journal of Applied Mathematics and Computing, 2017 This paper presents for the first time a robust exact line-search method based on a full pseudospectral (PS) numerical scheme employing orthogonal polynomials.
Elgindy, Kareem T.
core +3 more sources
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
doaj +3 more sources
Generalized Chebyshev Polynomials
Discussiones Mathematicae - General Algebra and Applications, 2018 Let h(x) be a non constant polynomial with rational coefficients. Our aim is to introduce the h(x)-Chebyshev polynomials of the first and second kind Tn and Un. We show that they are in a ℚ-vectorial subspace En(x) of ℚ[x] of dimension n.
Abchiche Mourad, Belbachir Hacéne
doaj +3 more sources
, 2012 In this overview paper a direct approach to q-Chebyshev polynomials and their elementary properties is given. Special emphasis is placed on analogies with the classical case.
Johann Cigler +2 more
core +2 more sources
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
doaj +1 more source
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
doaj +2 more sources
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
doaj +1 more source
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
doaj +1 more source
Asymptotics of Chebyshev polynomials, V. residual polynomials [PDF]
The Ramanujan Journal, 2021 We study residual polynomials, $R_{x_0,n}^{(\mathfrak{e})}$, $\mathfrak{e}\subset\mathbb{R}$, $x_0\in\mathbb{R}\setminus\mathfrak{e}$, which are the degree at most $n$ polynomials with $R(x_0)=1$ that minimize the $\sup$ norm on $\mathfrak{e}$. New are upper bounds on their norms (that are optimal in some cases) and Szeg --Widom asymptotics under ...
Jacob S. Christiansen +2 more
openaire +4 more sources
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
doaj +1 more source