Hayman direction of meromorphic functions (Q1902048)

If one denotes by \(n (r, \theta - \varepsilon, \theta + \varepsilon, g = a)\) the number of \(a\)-points of the meromorphic function \(g\) in the domain \(\{z \in \mathbb{C} \mid |z |< r\) and \(\theta - \varepsilon < \arg z < \theta + \varepsilon\}\) then it is proved that for a meromorphic function \(f\) with \[ \limsup_{r \to \infty} {T(r,f) \over (\log r)^2} = \infty \] there is \(\theta \in [0,2 \pi]\) such that for every \(\varepsilon > 0\) and positive integer \(\ell\)\ \ \(\lim_{r \to \infty} [n(r, \theta - \varepsilon, \theta + \varepsilon, f = a) + n (r, \theta - \varepsilon, \theta + \varepsilon, f^{(\ell)} = b)] = \infty\) for all \((a,b) \in \mathbb{C} \times (\mathbb{C} \backslash \{0\})\).