Math 6720 • Applied Complex Variables and Asymptotic Methods

\begin{enumerate}
\item
(10 pts) Show that
\[
\int_{-\infty}^{\infty}\frac{\cos x}{x^2-\frac{\pi^2}{4}}\,dx=-2.
\]

\item
(10 pts) Compute the complete infinite asymptotic expansion of
\[
I(k)=\int_0^\pi e^{-kt^2}t^{-3/4}\sin t\,dt.
\]
\end{enumerate}