This is documentation for Mathematica 7, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)


Residue[expr, {z, z0}]
finds the residue of expr at the point z=z0.
  • The residue is defined as the coefficient of (z-z0)^-1 in the Laurent expansion of expr.
  • Mathematica can usually find residues at a point only when it can evaluate power series at that point.
Illustrate Cauchy's theorem for the integral of a complex function:
Residues are not defined at branch points:
New in 2