# Answered: Converting between Schwarz-Christoffel formulas for disk and half-plane [duplicate]

Is there a way to conveniently use change of variables (e.g. with a Möbius transformation) in order to convert from a Schwarz-Christoffel integral of the form $$C_1 + C_2 \int _0^w \prod _{k=1}^n (\zeta - w_k)^{-\beta_k} \ d\zeta$$ that maps the closed unit disk onto a polygonal region to an analogous integral of the form $$C_3 + C_4 \int ^w \prod _{k=1}^{n-1} (\zeta - \xi_k)^{-\beta_k} \ d\zeta$$ that does the same for the upper half plane?
• Yeah, the answer is for sure already there. Key point: Sum of external angles is $2$, which is the power of the denominator in the derivative of a Möbius function that maps the plane to the disk. – bryanj Jun 28 '14 at 2:00