Category:Definitions/Holomorphic Functions

This category contains definitions related to Holomorphic Functions.
Related results can be found in Category:Holomorphic Functions.

Let $U \subseteq \C$ be an open set.

Let $f : U \to \C$ be a complex function.

Then $f$ is holomorphic in $U$ if and only if $f$ is differentiable at each point of $U$.

We also say that $f$ is complex-differentiable in $U$.