I'm working on a problem in complex analysis that I don't know how to approach. The problem is as follows:
Let the Bessel functions $J_n$, for integer $n$, be defined by
$$e^\left(\frac{w}{2}(z-\frac{1}{z}\right)=\sum_{n=-\infty}^{+\infty}J_{n}(w)z^n. $$
Show that
$$J_{n} = \frac{1}{2\pi}\int_{0}^{2\pi}\exp(iw\sin\theta-in\theta)d\theta. $$
Any pointers welcome - thanks!