I can't figure out how to take this integral. Looks pretty standard to me, but somehow can't find anything helpful in the literature:
$\int_0^{2\pi} d\phi\; (1-2 a \cos \phi + a^2)^{k+ (\kappa/2)} e^{-i( \ell - \kappa) \phi} $
MMA is stuck with it as well, which makes me suspicious if the closed form exists...
Any help with this is highly appreciated!