On conditions for convergence of Taylor-Dirichlet series in a convex domain - Krutigolova, Ye. K.; Mel'nik, Yu. I. (Ukrains’kyi Matematychnyi Zhurnal, 1994)
We establish necessary and sufficient conditions for the absolute convergence of the series $$\mathop \sum \limits_{v = 1}^∞ \sum\limits_{k = 0}^{m_v - I} {a_{v,k} z^k \exp (λ _v z)} $$ 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.