Residue

Residue[expr,{z,z0}]

finds the residue of expr at the point z=z0.

Details and Options

  • The residue is defined as the coefficient of (z-z0)^-1 in the Laurent expansion of expr.
  • The Wolfram Language can usually find residues at a point only when it can evaluate power series at that point.

Examples

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Basic Examples  (2)

Scope  (3)

Applications  (1)

Illustrate Cauchy's theorem for the integral of a complex function:

Possible Issues  (1)

Residues are not defined at branch points:

Introduced in 1991
 (2.0)