# pole

Let $U\subset \u2102$ be a domain and let $a\in \u2102$. A function $f:U\to \u2102$ has a *pole* at $a$ if it can be represented by a Laurent series^{} centered about $a$ with only finitely many terms of negative exponent; that is,

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

in some nonempty deleted neighborhood of $a$, with ${c}_{-n}\ne 0$, for some $n\in \mathbb{N}$. The number $n$ is called the *order* of the pole. A *simple pole ^{}* is a pole of order 1.

Title | pole |
---|---|

Canonical name | Pole |

Date of creation | 2013-03-22 12:05:56 |

Last modified on | 2013-03-22 12:05:56 |

Owner | djao (24) |

Last modified by | djao (24) |

Numerical id | 8 |

Author | djao (24) |

Entry type | Definition |

Classification | msc 30D30 |

Related topic | EssentialSingularity |

Defines | simple pole |

Defines | simple |