Function complex-differentiable at a point

This article defines a property that can be evaluated for a function on a (particular kind of) set, and a point in that set. A function satisfying the property at every point, it is termed a holomorphic function
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Definition

In one dimension

Let $U$ be a domain in $\mathbb {C}$ and $f:U\to \mathbb {C}$ be a function. Let $z_{0}\in U$. We say that $f$ is complex-differentiable at $z_{0}$ if the complex differential of $f$ at $z_{0}$ is well-defined.