Construction of Analytic Functions

We first study in detail a classical function using methods of the function theory of one complex variable, namely the Gamma function.

We treat the theorems of WEIERSTRASS and MITTAG-LEFFLER for the construction of analytic functions with prescribed zeros and respectively poles with specified principle parts.

We prove the REIMANN Mapping Theorem, which claims that an elementary domain D ≠ C can be conformally mapped onto the unit disk E. In this context we will once more review the Cauchy Integral Theorem, prove more general variants of it, and gain different topological characterizations of elementary domains as regions “without holes”.