Let U be a domain and let a. A function f:U has a pole at a if it can be represented by a Laurent seriesMathworldPlanetmath centered about a with only finitely many terms of negative exponent; that is,


in some nonempty deleted neighborhood of a, with c-n0, for some n. The number n is called the order of the pole. A simple poleMathworldPlanetmathPlanetmath 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