ResidueSum

ResidueSum[f, z] finds the sum of residues of the meromorphic function f with the variable z.

• ResidueSum[{f, cons}, z] finds the sum of residues of f within the solution set of the constraints cons.

Examples

Sum of all residues:

ResidueSum[1/(z^2 - 1), z]
(* 0 *)

With constraints:

ResidueSum[{1/z, Im[z] > 0}, z]

For a rational function:

ResidueSum[1/((z - 1)(z - 2)), z]

Please visit the official Wolfram Language Reference for more details.