Article
Ufa Mathematical Journal
Volume 3, Number 2, pp. 42-55
A convergence domain of exponential monoms series
Krivosheyeva O.A.
Download PDF
Article on MathNetAbstact
In the paper questions of convergence of exponential monomials series is studied. Exponenetial series, Dirichlet's series and power series are particular cases of these series. A description for the coefficients space of exponential monomials series which converge in given convex domain in comlex plane is obtained. The full analogue of Abel's theorem for these series is given with a natural restriction. In particular, results about continuation of convergence of exponential series follow from this analogue. Also a full analogue of Cauchy-Hadamard's theorem is obtained. In it a formula which allows to find the convergence domain of these series by their coefficients is obtained. The marked results involve as particular cases all famous earlier results connected to Abel and Cauchy-Hadamard's theorems for exponential series, Dirichlet's series and power series.