Complex analysis MOC

Residue

A residue of a meromorphic function at a Singular point is the value of the coëfficient of the Laurent series about .

Residues themselves can be used to calculate a contour integral using Cauchy's Residue Theorem.

Calculating residues

Cauchy's residue formula¹ states that if has a pole of order at , then

In many cases, using the Laurent series is easier than using this formula.

Often L'Hôpital's Rule is involved in calculating residues.

#state/develop | #lang/en | #SemBr