The Existence of Meromorphic Functions with Prescribed Poles and Principal Parts
Abstract: The Swedish mathematician Gösta Mittag-Leffler (1846-1927) is well-known for founding Acta Mathematica, the famous international mathematical journal. His mathematical contributions are connected chiefly with complex analysis. The Mittag-Leffler theorem which built on Karl Weierstrass' work asserts the existence of meromorphic function with prescribed poles and principal parts. The main purpose of this thesis is to make a well-organised note of the Mittag-Leffler theorem which plays a significant role in complex analysis. The Weierstrass theorem which prescribes the zeros of holomorphic functions will be proved by using the result of the Mittag-Leffler's theorem. Moreover, the concept of the Mittag-Leffler star, a starshaped open domain will also be defined and proved in detail.
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