Definition:Primitive (Calculus)/Complex

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:

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

Also known as

A primitive is also known as an antiderivative.

The term indefinite integral is also popular.

Also see

• Results about primitives can be found here.
• Results about complex integral calculus can be found here.

Sources

• 2001: Christian Berg: Kompleks funktionsteori: $\S 2.3$