2019
Том 71
№ 11

# On conditions for convergence of Taylor-Dirichlet series in a convex domain

Abstract

We establish necessary and sufficient conditions for the absolute convergence of the series $$\mathop \sum \limits_{v = 1}^\infty \sum\limits_{k = 0}^{m_v - I} {a_{v,k} z^k \exp (\lambda _v z)}$$ 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.

English version (Springer): Ukrainian Mathematical Journal 46 (1994), no. 11, pp 1744-1749.

Citation Example: Krutigolova Ye. K., Mel'nik Yu. I. On conditions for convergence of Taylor-Dirichlet series in a convex domain // Ukr. Mat. Zh. - 1994. - 46, № 11. - pp. 1576-1581.

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