Systems of complex variable polynomials related to classical systems of orthogonal polynomials

  • M. A. Sukhorolsky National University "Lviv Polytechnic"
  • O. V. Veselovska National University "Lviv Polytechnic"
  • V. V. Dostoina National University "Lviv Polytechnic"

Abstract

UDC 517.586+517.538.3

We investigate the properties of systems of complex variable polynomials represented as the contour integrals with kernel functions analytic at infinity.
Conditions for existence of functions associated with these polynomials and sufficient conditions of expansion of analytic functions into series in these polynomials are established.
Expansions of functions into series in classical orthogonal polynomials in a complex domain, integral representations for such polynomials, dependencies of monomials $z^n$ of these polynomials, and other relations can be obtained as the corollaries implied by our results.

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O. V. Veselovska, V. V. Dostoina, A system of functions biorthogonal with the derivatives of Chebyshev second-kind polynomials of a complex variable, J. Math. Sci., 249, № 5, 785 – 803 (2020). DOI: https://doi.org/10.1007/s10958-020-04973-0

Published
23.11.2021
How to Cite
Sukhorolsky , M. A., O. V. Veselovska, and V. V. Dostoina. “Systems of Complex Variable Polynomials Related to Classical Systems of Orthogonal Polynomials”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, no. 11, Nov. 2021, pp. 1516 -31, doi:10.37863/umzh.v73i11.6699.
Section
Research articles