Normal families and omitted functions Xuecheng PangDegui YangLawrence Zalcman 30D45normal familiesomitted functions Let $\mathcal{F}$ be a family of meromorphic functions on the plane domain $D$, all of whose zeros and poles are multiple. Let $h$ be a meromorphic function which does not vanish on $D$. If for each $f\in\mathcal{F}$, $f'(z)\not=h(z)$ for $z\in D$, then $\mathcal{F}$ is normal on $D$. Indiana University Mathematics Journal 2005 text pdf 10.1512/iumj.2005.54.2492 10.1512/iumj.2005.54.2492 en Indiana Univ. Math. J. 54 (2005) 223 - 236 state-of-the-art mathematics http://iumj.org/access/