The characteristic function of an infinite order meromorphic function and its derivative. (Q2744416)

Let \(f(z)\) be a meromorphic function of infinite order. If \(\sum_{a\neq\infty}\delta(a, f)= \alpha\) \((\alpha\geq 1)\), \(\delta(\infty, f)= 2-\alpha\), then for any \(k\in\mathbb{N}\), we haveNEWLINENEWLINE (1) \(T(r,f^{(k)})\sim((1- k)+ k\alpha)T(r, f)\);NEWLINENEWLINE (2) when \(\delta^{(l)}_0(\infty,f)= 1\), \(T(r, f^{(k)})\sim T(r, f)\).NEWLINENEWLINE The conditions of the above result are strong, too.