👉 In mathematics, a hypercatalectic region is a type of region in the complex plane that can be described as an open set where every point on the boundary of the region is either a pole or a zero of some holomorphic function. These functions are assumed to satisfy certain properties such as boundedness and holomorphy, which means they must have continuous partial derivatives and be defined on a simply connected domain. The hypercatalectic regions were first introduced by M. G. Fuchs