A simple pole of an analytic function 
is a pole of order one. That is,
extends to an analytic
function at 
with a nonzero value there. Alternatively, its principal
part is 
for some 
. It is called simple because a function
with a pole of order 
at 
can be written as the product of 
functions with simple poles at
.
Simple Pole
See also
Essential Singularity, PolePortions of this entry contributed by Todd Rowland
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Cite this as:
Weisstein, Eric W., with contributions by Todd Rowland. "Simple Pole." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SimplePole.html