Recursive function including Bessel functions

Question

I was wondering if anybody knows how to solve (numerically) the following recursive equation (found in http://dx.doi.org/10.1109/3.250392): $$E^{o}_{k}=\sum^{\infty}_{q=-\infty}J_{q-k}(2m)E^{o}_q,$$ with $J$ being the Bessel function of the first kind.

Answer 1

@ m_goldberg: Yes, I'd like to evaluate the above stated definition for a given $m$. One hint was to try it with inverse Fourier transformation but I have no clue how to do that either.