I'm looking for a closed form for any of the following 3D convolution integrals:
$$ A(k) = \int_{\mathbb{R}^3} d^3p |p|^{\nu} \exp(-\alpha|p|)|k-p|^\mu\exp(-\alpha|k-p|);$$
$$ B(k) = \int_{\mathbb{R}^3} d^3p |p|^{\nu} \exp(-\alpha|p|^2)|k-p|^\mu\exp(-\alpha|k-p|^2).$$
Here $|\cdot|$ is just the Euclidean norm and $\mu,\nu,\alpha$ are not necessarily integers (but let's assume the integral converges). I know that the first integral can be solved in 1D, because it's just a convolution of Gamma distributions.
Any help is greatly appreciated.