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

  • Ye. K. Krutigolova
  • Yu. I. Mel'nik

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.
Published
25.11.1994
How to Cite
KrutigolovaY. K., and Mel’nikY. I. “On Conditions for Convergence of Taylor-Dirichlet Series in a Convex Domain”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 46, no. 11, Nov. 1994, pp. 1576-81, https://umj.imath.kiev.ua/index.php/umj/article/view/5599.
Section
Short communications