International Journal of Mathematics and Mathematical Sciences
Volume 2 (1979), Issue 1, Pages 45-60
doi:10.1155/S0161171279000053

On the overconvergence of certain series

Abstract

In this work, we consider certain class of exponential series with polynomial coefficients and study the properties of convergence of such series. Then we consider a subclass of this class and prove certain theorems on the overconvergence of such a series, which allow us to determine the conditions under which the boundary of the region of convergence of this series is a natural boundary for the function f defined by this series.