There is an integral equation that shows up in scattering problems in electromagnetics where the kernel looks like this:
$$G(z, z') = \frac{1}{8\pi^2} \int_0^{2\pi}d\phi' g\left(z, z', \phi'\right)$$
where
$$g\left(z, z', \phi'\right) = \frac{\exp\left(-jk\sqrt{\left(z-z'\right)^2+4a^2\sin^2\left(\phi'/2\right)}\right)}{\sqrt{\left(z-z'\right)^2+4a^2\sin^2\left(\phi'/2\right)}}$$
and where $k$ is the free space wavenumber and $a>0$ is the radius of a wire in question.
Could someone help me write this integral as a contour integral?