Isn't there a general way to find the branch points of a complex function? I mean, one cannot just go around every point to see if the function is multi-valued. Isn't there some sort of classification letting know how to deal with functions of a special type?
Perhaps I'm asking this because I haven't digest the concept of branch point well. I've been reading that a branch point is a singularity, but don't understand the difference between a branch point and a singular point which is not a branch point! I know that the function is not continuous at a branch point; so it can't be analytic also, right?