In Complex Analysis, the Residue Theorem states that for a simple pole, the residue is equal to 

1
Limit as z approaches the pole of (z-z0) times the function.
2
Limit as z approaches infinity of (z-z0) times the function.
3
The coefficient of (z-z0)2 in the Laurent series.
4
The value of the function at the pole.
5
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