Just a quick question that I'm stuck on:

Let $\displaystyle \Gamma$ be the positively oriented circle with centre 0 and radius R. Show that

$\displaystyle \int_{\Gamma} \ z^{-2} e^{t(z + z^{-1})} dz = \sum_{m=0}^{\infty} \ b_{m} t^{2m+1} $

where the $\displaystyle b_{m}$ are constants you should calculate.

Is it not just a case of observing singularities and using Cauchy's Residue Theorem? Maybe there's something I'm missing but I'm stumped.

Thanks

pomp.