Monomials of entire algebroid functions (Q1276322)

A Hayman-Clunie theorem states that ``If \(f(z)\) is a transcendental entire function and \(n\geq 1\), then \(f(z)^{(n)}f'(z)\) assumes all values except possibly zero infinitely often'', \textit{J. Clunie} [J. Lond. Math. Soc. 42, 389-392 (1967; Zbl 0169.40801)]. The author extends this theorem to an entire algebroid function \(w\) and its monomials \(w^{n_0} (w')^{n_1} \dots (w^{(k)})^{n_k}\).