Estimates of the logarithmic derivative near a singular point and applications

Abstract

In this paper, we will give estimates for the logarithmic derivative $\left|\frac{f^{\left(k\right)}\left(z\right)}{f\left(z\right)}\right|$ where $f$ is a meromorphic function in a region of the form $D\left(0,R\right)=\left\{z\in \mathbb{C}:0<\left|z\right|<R\right\}.$ Some applications on the growth of solutions of linear differential equations near a singular point are given.

15 pages