I am working on a 2D Boundary Integral Method code for acoustics problems and I need to integrate singular kernels.
The functions that I have to deal with are:
$$ I_{1} = \int_{-1}^{1} H_0 ^{(1)}(r)dr $$ $$ I_{2} = \int_{-1}^{1} \frac{dH_0 ^{(1)}(r)}{dr}\frac{1}{r} dr $$
Is there any idea of how can I do that? I though about evaluating it using small argument approximations, but I can't find it anywhere.
Any help is much appreciated!