ThmDex – An index of mathematical definitions, results, and conjectures.
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Definition D5005
Complex function primitive
Formulation 1
Let $U \subseteq \mathbb{C}$ be a D5008: Standard open complex set such that
(i) $f : U \to \mathbb{C}$ is a D4881: Complex function on $U$
A D4881: Complex function $F : U \to \mathbb{C}$ on $U$ is a primitive for $f$ on $U$ if and only if
(1) $F$ is a D1392: Holomorphic function on $U$
(2) \begin{equation} \forall \, z \in U : F'(z) = f(z) \end{equation}
Also known as
Complex antiderivative function