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 .
See alsoCurve Divisor, Essential Singularity, Pole
This entry contributed by Todd Rowland
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Rowland, Todd. "Simple Pole." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/SimplePole.html