Math 6720 • Applied Complex Variables and Asymptotic Methods

Series and singularities
\begin{enumerate}
\item
(13 points) Expand the function
\[f(z)=\frac{z}{(z-2)(z+i)}\]
in a Laurent series in powers of \(z\) in \(1<|z|<2\).
\item
(12 points) Discuss the type of singularity (removable, pole and order, essential, branch,
cluster). If the type is a pole give the strength of the pole, and give the nature (isolated
or not). Include the point at infinity.
\[f(z)=\frac{e^{2z}-1}{z^2}\]
\end{enumerate}

\item