# Laurent series expansion of complex functions

For each of the functions f(z) find the Laurent Series expansion on for the given isolated singularity (specify R). Then classify as an essential singularity, a pole (specify the order), or a removable singularity. Then find

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suppose is an isolated singularity of f, then

is removable the Laurent expansion is a Taylor series - there are no negative powers of in the expansion.

is a pole of order n there are exactly n terms in the Laurent expansion with negative powers of

is an essential singularity there is infinite number of terms in the Laurent expansion with negative powers of

1.

(1.1)

There are two singularities for this ...

#### Solution Summary

The solution shows how to expand a complex function to a Laurent series, identify the type of singularity and find the residue.