SEARCH MATHEMATICA 8 DOCUMENTATION

THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.

Built-in Mathematica Symbol

Residue

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