The growth of meromorphic functions and their derivatives near a transcendental singularity

Abstract

In this work the question of the relation of the growth of a meromorphic function and that of its derivative is considered. In the plane J.M. Whittaker proved that and have the same order. Here it is shown that for meromorphic functions in the order of growth of and are the same at zero and infinity. This can also be extended to meromorphic functions , that is, meromorphic functions in the plane punctured at a finite number of points. A natural question is whether this always happens at a neighbourhood of a transcendental singularity. The answer to this question is unknown to the author.