Residue at infinity

In complex analysis, a branch of mathematics, the residue at infinity is a residue of a holomorphic function on an annulus having an infinite external radius. The infinity ${\displaystyle \infty }$ is a point added to the local space ${\displaystyle \mathbb {C} }$ in order to render it compact (in this case it is a one-point compactification). This space denoted ${\displaystyle {\hat {\mathbb {C} }}}$ is isomorphic to the Riemann sphere. One can use the residue at infinity to calculate some integrals.