Throughout this study, we continue the analysis of a recently found out Gibbs–Wilbraham phenomenon, being related to behavior Lagrange interpolation polynomials continuous absolute value function. Our study establishes error polynomial interpolants function |x| on [−1,1], using Chebyshev and Chebyshev–Lobatto nodal systems with an even number points. Moreover, respect odd cases, relevant change...

We characterize the generalized Chebyshev polynomials of the second kind (Chebyshev-II), and then we provide a closed form of the generalized Chebyshev-II polynomials using the Bernstein basis. These polynomials can be used to describe the approximation of continuous functions by Chebyshev interpolation and Chebyshev series and how to efficiently compute such approximations. We conclude the pap...

In this supplementary material, we give additional details on the two polynomial filters discussed in the main paper. First, we give an example to illustrate how the choice of the degree in the extend McWeeny filter method affects the inflexion point and the rank estimated. Next, we discuss some details on the practical implementation of the Chebyshev polynomial filter method. In section 4, we ...

Caution: These polynomials are referred to as w0, w1, w2, ... in Sections 5-8 of [1]. However, beginning with Section 9 of [1], Hazewinkel uses the notations w1, w2, w3, ... for some different polynomials (the so-called big Witt polynomials, defined by formula (9.25) in [1]), which are not the same as our polynomials w1, w2, w3, ... (though they are related to them: in fact, the polynomial wk t...

The eponymous theorem of P.L. Wantzel [Wan] presents a necessary and sufficient criterion for angle trisectability in terms of the third Chebyshev polynomial T3, thus making it easy to prove that there exist non-trisectable angles. We generalize this theorem to the case of all Chebyshev polynomials Tm (Corollary 1.4.1). We also study the set m-Sect consisting of all cosines of m-sectable angles...

Abstract—The edges of low contrast images are not clearly distinguishable to human eye. It is difficult to find the edges and boundaries in it. The present work encompasses a new approach for low contrast images. The Chebyshev polynomial based fractional order filter has been used for filtering operation on an image. The preprocessing has been performed by this filter on the input image. Laplac...

In this paper, we introduce the class of $(\beta,\gamma)$-Chebyshev functions and corresponding points, which can be seen as a family {\it generalized} Chebyshev polynomials points. For functions, prove that they are orthogonal in certain subintervals $[-1,1]$ with respect to weighted arc-cosine measure. particular investigate cases where become polynomials, deriving new results concerning clas...

We give formulas for the Tutte polynomials of parallel and series connections of weightedmatroids, generalizing and unifying formulas of Oxley and Welsh (Discrete Math. 109 (1992) 185), Bollobás and Riordan (Comb. Probab. Comput. 8 (1999) 45) and Woodall (Discrete Math. 247 (2002) 201). © 2004 Elsevier B.V. All rights reserved.

We develop complex Jacobi, Gegenbauer and Chebyshev polynomial expansions for the kernels associated with power-law fundamental solutions of the polyharmonic equation on d-dimensional Euclidean space. From these series representations we derive Fourier expansions in certain rotationally-invariant coordinate systems and Gegenbauer polynomial expansions in Vilenkin’s polyspherical coordinates. We...

For the Hahn and Krawtchouk polynomials orthogonal on the set {0, . . . , N} new identities for the sum of squares are derived which generalize the trigonometric identity for the Chebyshev polynomials of the first and second kind. These results are applied in order to obtain conditions (on the degree of the polynomials) such that the polynomials are bounded (on the interval [0, N ]) by their va...