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This question already has an answer here:

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?

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marked as duplicate by user147263, bryanj, Moishe Kohan, mathematics2x2life, user91500 Jun 28 '14 at 4:16

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  • $\begingroup$ 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. $\endgroup$ – bryanj Jun 28 '14 at 2:00
  • $\begingroup$ @Thisismuchhealthier. : Should I just delete it myself? Don't know what the protocol is. Thx. $\endgroup$ – bryanj Jun 28 '14 at 2:03
  • $\begingroup$ I think it's better to keep it as a duplicate, because your statement of the question is more to the point (hence, searchable) than the other one. $\endgroup$ – user147263 Jun 28 '14 at 2:08

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