Definition:Reversed Contour

Definition
Let $\R^n$ be a real cartesian space of $n$ dimensions.

Let $C$ be a contour in $\R^n$.

Then $C$ is defined as a concatenation of a finite sequence $C_1, \ldots, C_n$ of directed smooth curves in $\R^n$.

The reversed contour of $C$ is denoted $-C$ and is defined as the concatenation of the finite sequence:


 * $-C_n, -C_{n - 1}, \ldots, -C_1$

where $-C_i$ is the reversed directed smooth curve of $C_i$ for all $i \in \set {1, \ldots, n}$.

Complex Plane
The definition carries over to the complex plane, in which context it is usually applied:

Also denoted as
The reversed contour of $C$ is denoted as $C^-$ in some texts.

Also see

 * Reversed Contour is Contour: demonstration that this defines a contour.