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
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): singular point (singularity): 1.
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): singular point (singularity): 1.