On the value distribution of \(ff^{(k)}\)
If \(g\) is a transcendental entire function of finite order, then there exists at most one integer \(k\geq 2\), such that \(ff^{(k)}\) has a nonzero and finite Picard exceptional value. If \(f\) is a transcendental meromorphic function, we have that 1) for nonnegative integers \(n,n_1, \dots, n_k\) with \(n\geq 1\), \(d=n_1+ \cdots +n_k\geq 1\), if \(\delta\) \((0,f)> 3/(3d +1)\), then \(f^n(f')^{n_1} \dots (f^{(k)})^{n_k}\) has no finite nonzero Picard exceptional value. 2) under certain conditions, for \(c\in \mathbb{R}\setminus\{0\}\), \[ T(r,f)\leq \left(4+{1 \over k+1}\right) \left\{\overline N(r,f)+ \overline N \left(r, {1\over fP(f)-c} \right)\right\} +S(r,f), \] where \(P(f)\) is a class of differential polynomials.
scientific article; zbMATH DE number 949858