According to Riemann's mapping theorem, there exists a biholomorphic equivalence between any two simply connected domains that are not equal to the whole complex plane. In the work of the diploma seminar, we will examine the theorem in special case, where the bijective holomorphic mapping can be explicitly expressed. The Schwarz-Christoffel mapping is a complex function that maps the upper half plane to the interior of any polygon. In the assigment, we will find and justify its formula and at the end, give some simple examples of biholomorphic transformations.
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