Let Omega = C\((-inf,-1]U[1,inf)), find a holomorphic bijection phimega-->delta, where delta is the open unit disk
Reimann Mapping Theorem
Special Mapping formulas: can map wedges onto wedges, with deletion of real line from zero to infinity in order to deal with log.
The unique bilinear mapping that sends 3 points onto; inf,0,1.
The Attempt at a Solution
so what this looks like, is all of C besides for the parts on the real line that goes from -inf to 1 and 1 to inf. also, if we consider C-hat and the point at infinity we can see that this is a simply connected domain and so by Reimann Mapping Theorem there exists a bijection between it and every other simply connected domain(of which delta is one). so, in its present form this domain is unworkable. so i want to somehow map it onto the real line from 0 to inf from which i can go from there. like i said, i know the unique bilinear mapping but that is for 3 discrete points, which does not work in this case since i have the whole line. also, i need it to be 1 to 1, since it must be a bijection and i already have a point at 1 and infinity.