meromorphic extension

Let AB and f:A be analytic. A meromorphic extension of f is a meromorphic function g:B such that g|A=f.

The meromorphic extension of an analytic function to a larger domain ( is unique; i.e. (, using the above notation, if h:B 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 functionDlmfDlmfMathworldPlanetmath.

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