# technique for computing residues

The following two facts are quite useful for computing residues:

If $f$ has a pole of order at most $n+1$ at $x$, then

 $\operatorname{Res}(f;x)=\lim\limits_{y\to x}{1\over n!}{d^{n}\over dy^{n}}% \left((y-x)^{n+1}f(y)\right).$

If $g$ is regular at $x$ and $f$ has a simple pole at $x$, then $\operatorname{Res}(fg;x)=g(x)\operatorname{Res}(f;x)$.

Title technique for computing residues TechniqueForComputingResidues 2013-03-22 16:20:11 2013-03-22 16:20:11 rspuzio (6075) rspuzio (6075) 7 rspuzio (6075) Theorem msc 30D30 CoefficientsOfLaurentSeries ResiduesOfTangentAndCotangent