simple pole

A simple pole is a pole of order 1. That is, a meromorphic function $f$ has a simple pole at$x_0\in ℂ$ if

$$f(z)=\frac{a}{z-x_0}+g(z)$$

where $a\ne 0\in ℂ$, and $g$ is holomorphic at $x_0$.

Note that $a$ in the equation above is the residue of $f$ at $x_0$.