Semicircular contour

Definition

A semicircular contour of radius $R$ is a contour comprising:

• A semicircle of radius $R$, centered at the origin, and in the upper half-plane
• The diameter of this semicircle, joining the points $R$ and $-R$

Semicircular contours are often used to compute integrals along the real line; for this, we take the limit as $R\to \mathrm{\infty }$.

Further information: semicircular contour integration method