On Natural Boundaries of a Generalized Lambert Series

Abstract

and showed that any analytic function can be represented in this form plus a constant. Doyle [2] determined, the regions of convergence, expansion in power series and the inversion of power series into a generalized Feld series, which included (1) as a special case. It is the purpose of this paper to investigate the Feld series for natural boundaries. In establishing natural boundaries for this series, conditions on the sequences {an} and {bn} of (1)) are determined. Before obtaining these conditions three theorems dealing with natural bound aries of the Lambert series