Convergence regions for continued fractions
Thron, Wolfgang J.
Doctor of Philosophy
This thesis contains the results of a new approach to the problem of finding sufficient conditions for the convergence of continued fractions with complex elements. New convergence criteria are obtained for all three of the most commonly studied types, namely (1) b0 + K(1/bn), (2) 1 + K(an/1), (3) K(an /bn). Our convergence theorems are of the convergence region type. Certain convergence regions have been known for some time. Worpitzky's criterion for continued fractions and Van Vleck's and Pringsheim's theorems for continued fractions are of this type.