A simple pole of an analytic function 
is a pole of order one. That is,
is an analytic
function at the pole 
.
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, PoleThis entry contributed by Todd Rowland
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Cite this as:
Rowland, Todd. "Simple Pole." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/SimplePole.html