Residue[expr, x, ] finds the residue of expr at the point .
The residue is defined as the coefficient of (x - )^-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.
See The Mathematica Book: Section 3.6.9.
See also: Series, Limit, PrincipalValue.
Related package: Algebra`RootIsolation`.