Definition:Differentiable Mapping/Complex Function/Region
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Definition
Let $D \subseteq \C$ be an open set.
Let $f: D \to \C$ be a complex function.
Then $f$ is complex-differentiable in $D$ if and only if $f$ is complex-differentiable at every point in $D$.
Also known as
A function which is complex-differentiable in an open set is called a holomorphic function in many texts.
It is also referred to as an analytic function.
Sources
- 2001: Christian Berg: Kompleks funktionsteori: $\S 1.1$