# simple pole

A *simple pole ^{}* is a pole of order 1. That is, a meromorphic function $f$ has a simple pole at
${x}_{0}\in \u2102$ if

$$f(z)=\frac{a}{z-{x}_{0}}+g(z)$$ |

where $a\ne 0\in \u2102$, and $g$ is holomorphic at ${x}_{0}$.

Note that $a$ in the equation above is the residue of $f$ at ${x}_{0}$.

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

Canonical name | SimplePole |

Date of creation | 2013-03-22 13:15:55 |

Last modified on | 2013-03-22 13:15:55 |

Owner | bwebste (988) |

Last modified by | bwebste (988) |

Numerical id | 7 |

Author | bwebste (988) |

Entry type | Definition |

Classification | msc 30D30 |