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

Authors

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

DOI:

https://doi.org/10.37863/umzh.v73i11.6699

Keywords:

ортогональні поліноми, біортогональні системи функцій, асоційована функція

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 zn of these polynomials, and other relations can be obtained as the corollaries implied by our results.

References

A. I. Markushevich, Izbrannyie glavyi teorii analiticheskih funktsiy, Nauka, Moskva(1976).

S. Pashkovskiy, Vyichislitelnyie primeneniya mnogochlenov i ryadov Chebyishova, Nauka, Moskva (1983).

G. Polia, G.Sege, Problems and theorems in analysis. Part One, Nauka, Moscow (1978).

A. P. Prudnikov, Yu. A. Bryichkov, O. I. Marichev, Integralyi i ryadyi. Elementarnyie funktsii, Nauka, Moscow (1981).

G.Sege, Ortogonalnyie mnogochlenyi, Fizmatgiz, Moskva (1962).

M. A. Suhorolskiy, Rozvinennya funktsiy za sistemoyu polinomiv, biortogonalnih na zamknenomu konturi z sistemoyu regulyarnih u neskinchenno viddaleniy tochtsi funktsiy, Ukr. mat. zhurn., 62, № 2, 238 – 254 (2010).

M. A. Sukhorolskyi, Nablyzhennia funktsii polinomamy Lezhandra v kompleksnii ploshchyni , Visn. Nats. un-tu „Lviv. politekhnika”, № 643, 3 – 14 (2009).

M. A. Sukhorolskyi, V. V. Dostoina, Rozklad analitychnykh v kruzi funktsii v kompleksnii oblasti za systemoiu pokhidnykh mnohochleniv Lezhandra, Visn. Nats. un-tu „Lviv. politekhnika”, № 687, 105 – 121 (2010).

M. A. Sukhorolskyi, V. V. Dostoina, O. V. Veselovska, Mnohochleny, sporidneni z mnohochlenamy Chebyshova, Prykl. problemy mekhaniky i matematyky, 15, 35 – 41 (2017).

M. A. Sukhorolskyi, V. V. Dostoina, O. V. Veselovska, Systema funktsii, biortohonalna z mnohochlenamy, sporidnenymy z mnohochlenamy Chebyshova, Visn. Kyiv. nats. yn–tu im. T. Shevchenka. Matematyka, mekhanika, № 1, 53 – 59 (2018).

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

Issue

Section

Research articles

How to Cite

Sukhorolsky , M. A., et al. “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, https://doi.org/10.37863/umzh.v73i11.6699.