# 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

$$\mathrm{Res}(f;x)=\underset{y\to x}{lim}\frac{1}{n!}\frac{{d}^{n}}{d{y}^{n}}\left({(y-x)}^{n+1}f(y)\right).$$ |

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

Title | technique for computing residues |
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Canonical name | TechniqueForComputingResidues |

Date of creation | 2013-03-22 16:20:11 |

Last modified on | 2013-03-22 16:20:11 |

Owner | rspuzio (6075) |

Last modified by | rspuzio (6075) |

Numerical id | 7 |

Author | rspuzio (6075) |

Entry type | Theorem |

Classification | msc 30D30 |

Related topic | CoefficientsOfLaurentSeries |

Related topic | ResiduesOfTangentAndCotangent |