# simple pole

A simple pole is a pole of order 1. That is, a meromorphic function $f$ has a simple pole at $x_{0}\in\mathbb{C}$ if

 $f(z)=\frac{a}{z-x_{0}}+g(z)$

where $a\neq 0\in\mathbb{C}$, 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 SimplePole 2013-03-22 13:15:55 2013-03-22 13:15:55 bwebste (988) bwebste (988) 7 bwebste (988) Definition msc 30D30