Transcendental singularities for a meromorphic function with logarithmic derivative of finite lower order

TL;DR

This paper refines existing results on transcendental singularities for meromorphic functions by showing that certain properties hold under the weaker condition that the logarithmic derivative has finite lower order.

Contribution

It demonstrates that key results on transcendental singularities extend to functions with finite lower order of their logarithmic derivatives, relaxing previous assumptions.

Findings

Refined conditions for transcendental singularities

Extension of key results to functions with finite lower order

Weaker hypotheses suffice for established theorems

Abstract

In this note it is shown that two key results on transcendental singularities for meromorphic functions of finite lower order have refinements which hold under the weaker hypothesis that the logarithmic derivative has finite lower order.