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604  Articles
1 of 61 pages  |  10  records  |  more records»
We construct a system of functions biorthogonal with Chebyshev polynomials of the second kind on closed contours in the complex plane. Properties of these functions and sufficient conditions of expansion of analytic functions into series in Chebyshev poly... see more

Properties of the derivatives of polynomials of a complex variable that are related to Chebyshev polynomials and conditions of expansion of analytic functions in circle into series by them are investigated. Examples of such expansions are presented.

The aim of this paper is to make an explicit link between the Weyl-orbit functions and the corresponding polynomials, on the one hand, and to several other families of special functions and orthogonal polynomials on the other. The cornerstone is the conne... see more

Exact inequalities of Jackson's type, connected with the best approximation of functions by algebraic polynomials, have been obtained in the space L2,?(R)L_{2,\rho}(\mathbb{R}) at the Chebyshev-Hermite weight.

We apply the polynomial method—specifically, Chebyshev polynomials—to obtain a number of new results on geometric approximation algorithms in low constant dimensions. For example, we give an algorithm for constructing e-kernels (coresets for approximate w... see more

We prove various formulas which express exponential generating functions counting permutations by the peak number, valley number, double ascent number, and double descent number statistics in terms of the exponential generating function for Chebyshev poly... see more

We discuss technical issues involving the implementation of a computational method for the electronic structure of material systems of arbitrary atomic arrangement. The method is based on the analysis of time evolution of electron states in the real latti... see more

In this paper, we present efficient direct solver for solving the generalized pantographequations with variable coefficients. The approach is based on the second kind Chebyshev polynomialstogether with operational method. The main characteristic behind th... see more

Sharp inequalities of Jackson type, connected with the best approximation by "angles" of algebraic polynomials have been obtained on the classes of differentiable functions of two variables in the metric of space L2;?(R2)L_{2;\rho}({\mathbb{R}}^2) of the ... see more

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