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This is a problem I am stuck at. I think this problem has to do with Riemann mapping theorem and Schwarz reflection principle, but I cannot find a way to solve it... Could anyone please help me how to solve this problem?

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  • $\begingroup$ Look at $g \colon z \mapsto \overline{f(\overline{z})}$. What do you know about $g$? $\endgroup$ – Daniel Fischer Oct 9 '17 at 11:08
  • $\begingroup$ All I can see is that $g$ is another analytic function. Could you tell me what I am missing? $\endgroup$ – Keith Oct 9 '17 at 12:01
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    $\begingroup$ See this question and this one. $\endgroup$ – Daniel Fischer Oct 9 '17 at 12:11

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