I have a pretty ferocious integral to solve, and since it doesn't seem I'll be able to do much analytically, I've taken to Mathematica to get some information. Mainly, I want to see if there are any constant terms in the following integral:

$$ I = \int_{r}^{\infty} r_0^{-5/2} W_{-i\alpha'/2, \nu}(\frac{-ir_0^2\omega'}{L}) W_{-i\alpha/2, \nu}(\frac{-ir_0^2\omega}{L}) J_{\nu}(-i\hat{k}r_0) dr_0$$

Where W is WhittakerW, J is BesselJ, and everything besides r/r_0 is a constant.

So far, I've simply been doing NIntegrate and breaking the integral up over several pieces. I plotted the function on a log plot, and it seems after about r ~ 10 it drops off significantly; as such, the integral from 10 to infinity seems to be zero. After this, I've just plotted the integral and tried to look at dependence using LogPlots. Does anyone have a better method to deal with Numerical Integrals like this to get a bit more information?