Abstract
We establish necessary and sufficient conditions for the absolute convergence of the series
in an open region. We also give conditions under which an arbitrary function analytic in a closed region (analytic in an open region and continuous in a closed region) can be represented by a series of this type.
References
A. F. Leont'ev,Series of Exponents [in Russian], Nauka, Moscow (1976).
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Deceased.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol.46, No. 11, pp. 1576–1580, November, 1994.
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Krutigolova, E.K., Mel'nik, Y.I. On conditions for convergence of Taylor-Dirichlet series in a convex domain. Ukr Math J 46, 1744–1749 (1994). https://doi.org/10.1007/BF01058894
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DOI: https://doi.org/10.1007/BF01058894