I am trying to determine a function that maps (preferably conformal map) that maps an infinite strip is the 2nd quadrant, between $y=\pi/6, 7\pi/6$, to a half disk (upper plane, quad 1/2) of radius one, centered at the origin.
Any help would be appreciated!
To get started, I'm guessing the map would be an exponential map or something of that sort. If so, how would I continue? Just a little confused on the problem and such.