Function that transforms (half) plane to annulus

[meldraft]

Hey all,

I am looking for a complex function that conformally transforms a part of the plane (don't really care which part, as long as it's a polygon (even with infinite sides)) to an annulus (that is, a disk with a hole in the middle). My books on complex analysis conveniently skip it, but I'm pretty sure it must exist. Does anyone know of such a function??

 

[meldraft]

Nevermind, found it

In case another person is interested, it's exp(z), but the size of the domain must be 2*pi, otherwise the domain overlaps with itself