# meromorphic extension

Let $A\subset B\subseteq \u2102$ and $f:A\to \u2102$ be analytic. A meromorphic extension of $f$ is a meromorphic function $g:B\to \u2102$ such that ${g|}_{A}=f$.

The meromorphic extension of an analytic function to a larger domain (http://planetmath.org/Domain) is unique; i.e. (http://planetmath.org/Ie), using the above notation, if $h:B\to \u2102$ has the property that ${h|}_{A}=f$, then $g=h$ on $B$.

Occasionally, an analytic function and its meromorphic extension are denoted using the same notation. A common example of this phenomenon is the Riemann zeta function^{}.

Title | meromorphic extension |
---|---|

Canonical name | MeromorphicExtension |

Date of creation | 2013-03-22 16:07:26 |

Last modified on | 2013-03-22 16:07:26 |

Owner | Wkbj79 (1863) |

Last modified by | Wkbj79 (1863) |

Numerical id | 10 |

Author | Wkbj79 (1863) |

Entry type | Definition |

Classification | msc 30D30 |

Synonym | meromorphic continuation |

Related topic | AnalyticContinuationOfRiemannZeta |

Related topic | RestrictionOfAFunction |