Pole (Complex Analysis)/Examples/Reciprocal of (z-3)^2 (z+1)

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Examples of Poles in the context of Complex Analysis

Let $f$ be the complex function:

$\forall z \in \C \setminus \set {-1, 3}: \map f z = \dfrac 1 {\paren {z - 3}^2 \paren {z + 1} }$

Then $f$ has:

a pole of order $2$ at $z = 3$
a simple pole at $z = -1$.


Sources