Systems of complex variable polynomials related to classical systems of orthogonal polynomials - Sukhorolsky , M. A.; Veselovska , O. V.; Dostoina , V. V. (Ukrains’kyi Matematychnyi Zhurnal, 2021)
UDC 517.586+517.538.3We 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.