On the spherical derivative of an entire function (Q1077584)

Let f be a transcendental entire function of order \(\lambda\). Denote by \(\mu\) (r,f) the maximum value of the spherical derivative of f on the circle \(| z| =r\). If \(\lambda <\) then \[ \lim \inf_{r\to \infty}(\log \mu (r,f)/\log M(r,f))\leq -\cos \pi \lambda \] and this estimate is the best possible.