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Ufa Mathematical Journal, 2011, Volume 3, Issue 2, Pages 42–55 (Mi ufa93)  

This article is cited in 20 scientific papers (total in 20 papers)

The convergence domain for series of exponential monomials

O. A. Krivosheyeva

Bashkir State University, Ufa, Russia
References:
Abstract: Questions of convergence for exponential series of monomials are studied in this paper. Exponential series, Dirichlet's series and power series are particular cases of these series. The space of coefficients of exponential series of monomials converging in the given convex domain in a complex plane is described. The full analogue of Abel's theorem for these series is formulated with a natural restriction. In particular, results on continuation of convergence of exponential series follow from this analogue. A full analogue of Cauchy–Hadamard's theorem is obtained as well. It provides a formula for finding the convergence domain of these series by their coefficients. The obtained results include all earlier known results connected with Abel and Cauchy–Hadamard's theorems for exponential series, Dirichlet's series and power series as particular cases.
Keywords: exponential series, convex domain, analytic function.
Received: 08.11.2010
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: English
Original paper language: Russian
Citation: O. A. Krivosheyeva, “The convergence domain for series of exponential monomials”, Ufa Math. J., 3:2 (2011), 42–55
Citation in format AMSBIB
\Bibitem{Kri11}
\by O.~A.~Krivosheyeva
\paper The convergence domain for series of exponential monomials
\jour Ufa Math. J.
\yr 2011
\vol 3
\issue 2
\pages 42--55
\mathnet{http://mi.mathnet.ru//eng/ufa93}
\zmath{https://zbmath.org/?q=an:1249.30005}
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  • This publication is cited in the following 20 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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