# residue

Let $U\subset \u2102$ be a domain and let $f:U\u27f6\u2102$ be a function represented by a Laurent series^{}

$$f(z):=\sum _{k=-\mathrm{\infty}}^{\mathrm{\infty}}{c}_{k}{(z-a)}^{k}$$ |

centered about $a$. The coefficient ${c}_{-1}$ of the above Laurent series is called the *residue* of $f$ at $a$, and denoted $\mathrm{Res}(f;a)$.

Title | residue |
---|---|

Canonical name | Residue |

Date of creation | 2013-03-22 12:04:56 |

Last modified on | 2013-03-22 12:04:56 |

Owner | djao (24) |

Last modified by | djao (24) |

Numerical id | 7 |

Author | djao (24) |

Entry type | Definition |

Classification | msc 30D30 |

Related topic | CauchyResidueTheorem |