Normal families of zero-free meromorphic functions (Q448848)

Summary: Let \(a, b \in \mathbb C\), \(a\neq 0\), and \(n\) and \(k\) be two positive integers such that \(n \geq 2\). Let \(\mathcal F\) be a family of zero-free meromorphic functions defined in a domain \(\mathcal D\) such that for each \(f \in \mathcal F\), \(f + a(f^{(k)})^n - b\) has at most \(nk\) zeros, ignoring multiplicity. Then \(\mathcal F\) is normal in \(\mathcal D\).