Logarithmic derivative

Let \(\Omega\subseteq\CC\) be open and let \(f\) be meromorphic on \(\Omega\) and not identically zero on any connected component of \(\Omega\). The logarithmic derivative of \(f\) is the meromorphic function \[ \logd f\coloneqq\frac{f'}{f} \] on \(\Omega\).