Residue

Residue[expr, {z, z0}] finds the residue of expr at the point z = z0.

Examples

Find the residue of a simple pole:

Residue[1/z, {z, 0}]
(* 1 *)

Residue at a higher-order pole:

Residue[1/z^3, {z, 0}]
(* 0 *)

Residue[1/(z - 1)^2, {z, 1}]
(* 0 *)

Please visit the official Wolfram Language Reference for more details.