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 _v = 1^∞ _k = 0^m_v - I a_v,k z^k (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.