Properties of the second-kind Chebyshev polynomials of complex variable

O.V. Veselovska; V.V. Dostoina; M.I. Klapchuk

doi:10.15421/242009

Properties of the second-kind Chebyshev polynomials of complex variable

O.V. Veselovska (Lviv Polytechnic National University), https://orcid.org/0000-0003-4052-1081
V.V. Dostoina (Lviv Polytechnic National University), https://orcid.org/0000-0002-7855-1094
M.I. Klapchuk (Lviv Polytechnic National University), https://orcid.org/0000-0003-4826-0824

Abstract

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 polynomials of the second kind in complex domains are investigated. The examples of such expansions are given. In addition, combinatorial identities of self-interest are obtained.

Keywords

Chebyshev polynomials; analytic functions; biorthogonal systems of functions; associated functions

MSC 2020

33E20; 33D45

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