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International Journal of Mathematics and Mathematical Sciences
Volume 2 (1979), Issue 1, Pages 45-60

On the overconvergence of certain series

Institut Fourier, Mathématiques Pures, Boite postale 116, St Martin d'Heres 38402, France

Received 27 April 1978

Copyright © 1979 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.