Definition:Primitive (Calculus)/Complex

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Definition

Let $F: D \to \C$ be a complex function which is complex-differentiable on a connected domain $D$.

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


Let:

$\forall z \in D: \map {F'} z = \map f z$

where $F'$ denotes the derivative of $F$ with respect to $z$.


Then $F$ is a primitive of $f$, and is denoted:

$\displaystyle F = \int \map f z \rd z$


Also known as

A primitive is also known as an antiderivative.

The term indefinite integral is also popular.


Also see

  • Results about complex integral calculus can be found here.


Sources