From the Riemann mapping theorem we know that there exists a biholomorphism between the rectangle $R$ and the unit disk $D$, can we write this biholomorphic map explicitly?
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3$\begingroup$ en.wikipedia.org/wiki/Schwarz%E2%80%93Christoffel_mapping $\endgroup$– Emil JeřábekMar 31, 2016 at 19:30
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$\begingroup$ Ah, Emil beat me to it by 30 secs ;-) so deleting my previous comment! $\endgroup$– SuvritMar 31, 2016 at 19:31
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$\begingroup$ (While the Wikipedia article presents a biholomorphism from a half-plane rather than from a disk, this is easy to fix with a Möbius transformation.) $\endgroup$– Emil JeřábekMar 31, 2016 at 19:44
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