In wikipedia, I found that a branch cut can be thought of as a sum of infinitely many poles arranged along a line in the complex plane with infinitesimal residues. And wiki takes $ln(\frac{z+1}{z-1})$ for an example. See Continuum of poles.
This is quite an interesting interpretation to me. So I am wondering if there is any similiar way to explain the branch cut of $\sqrt{\frac{z+a}{z+b}}$? Like writting it into a integral manner?