Mousehole contour

Definition

The mousehole contour with inner radius $r$ and outer radius $R>r$ comprises the following three pieces:

• A semicircle of radius $r$, centered at the origin, and in the upper half-plane
• A semicircle of radius $R$, centered at the origin, and in the upper half-plane
• Line segments joining the ends of these semicircles: one joining $r$ to $R$, and one joining $-r$ to $-R$.

There are more general versions of this; for instance, the quadrant mousehole contour, which comprises two concentric quadrants with joining line segments at the ends.

The mousehole contour is used as a tool in computing integrals of real-valued functions. For this, we let the inner radius tend to zero and the outer radius tend to $\mathrm{\infty }$.

Further information: mousehole contour integration method