The logarithmic derivative of a meromorphic function

A well-known lemma on the logarithmic derivative for a function f(z), f(0) = 1 (0 < r=">m( r,fracf￠f ) < ln+ { fracT(r,f)rfracrr- r } + 5.8501.mleft( {r,frac{{f'}}{f}} right)< ln + left{ {frac{{T(rho ,f)}}{r}frac{rho }{{rho - r}}} right} + 5.8501.