On functions defined by a Taylor series
Cowling, Vincent Frederick
Doctor of Philosophy
This thesis consists in greater part (Theorem B to Theorem K) of a number of new results which state conditions that a function defined by a Taylor series be of a certain form. In particular Theorems I and K are concerned with the form of certain entire functions. In Theorem L we prove a new result similar in nature to the composition theorems of Hadamard and Hurwitz. The last result is Theorem M. In this theorem a new necessary condition is given that a function defined by a Taylor series have one singularity in the finite plane.