In the field of integral equations, specifically boundary element methods, we often deal with integrals containing weak, strong, and hyper singularities. For a 2D integral, the singularities look like 1/r (weakly singular), 1/r^2 (strongly singular), and 1/r^3 (hypersingular). For a 1D integral, its ln(r) (weak), 1/r (strong), 1/r^2 (hyper).
I'm looking for some kind of formal definition of these singularities, and a reference that I can cite for it. I do understand that the strongly singular and hypersingular kernels only legitimately exist as CPV and HFP integrals, but I don't have any more depth than that.
This is my first post on stack exchange, so sorry if my post is incorrect in some way.