The Existence of Meromorphic Functions with Prescribed Poles and Principal Parts
(2020) In Bachelor’s Theses in Mathematical Sciences MATK11 20201Mathematics (Faculty of Engineering)
Mathematics (Faculty of Sciences)
 Abstract
 The Swedish mathematician Gösta MittagLeffler (18461927) is wellknown for founding Acta Mathematica, the famous international mathematical journal. His mathematical contributions are connected chiefly with complex analysis. The MittagLeffler 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 wellorganised note of the MittagLeffler 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 MittagLeffler's theorem. Moreover, the concept of the MittagLeffler star, a starshaped open domain... (More)  The Swedish mathematician Gösta MittagLeffler (18461927) is wellknown for founding Acta Mathematica, the famous international mathematical journal. His mathematical contributions are connected chiefly with complex analysis. The MittagLeffler 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 wellorganised note of the MittagLeffler 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 MittagLeffler's theorem. Moreover, the concept of the MittagLeffler star, a starshaped open domain will also be defined and proved in detail. (Less)  Popular Abstract
 We summarise some of the important concepts and results.
The Swedish mathematician Gösta MittagLeffler (18461927) was one of the most influential researchers in Swedish mathematics. His mathematical contributions are connected chiefly with complex analysis. He studied with Karl Weierstrass while he travelled to Berlin and some of his research were built on Weierstrass' work, such as the MittagLeffler theorem which is the main topic of this paper.
The MittagLeffler theorem proves the existence of meromorphic functions with prescribed poles and principal parts. Interestingly, this study began as an extension of the Weierstrass theorem. As a continuation of Weierstrass's work, it was undertaken with the tools acquired from... (More)  We summarise some of the important concepts and results.
The Swedish mathematician Gösta MittagLeffler (18461927) was one of the most influential researchers in Swedish mathematics. His mathematical contributions are connected chiefly with complex analysis. He studied with Karl Weierstrass while he travelled to Berlin and some of his research were built on Weierstrass' work, such as the MittagLeffler theorem which is the main topic of this paper.
The MittagLeffler theorem proves the existence of meromorphic functions with prescribed poles and principal parts. Interestingly, this study began as an extension of the Weierstrass theorem. As a continuation of Weierstrass's work, it was undertaken with the tools acquired from Weierstrass' lectures. These facts also show that MittagLeffler was indeed an important contributor to Weierstrass's research program concerning the foundations of analysis.
MittagLeffler published the final version of the theorem in 1884, in his newlyestablished journal Acta Mathematica which served as a comprehensive account of essentially all of his work on the subject. The theorem was seen as an important and fundamental element in complex analysis. It generated a number of research in the following generation of mathematicians, including the wellknown figures Picard, Appell, and Poincaré, and it remained popular and widelystudied in different languages, such as French, Russian and German. (Less)
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http://lup.lub.lu.se/studentpapers/record/9024200
 author
 Liu, Peicen ^{LU}
 supervisor

 Nils Dencker ^{LU}
 organization
 course
 MATK11 20201
 year
 2020
 type
 M2  Bachelor Degree
 subject
 keywords
 The MittagLeffler Theorem, Meromorphic Function, Complex Analysis, The MittagLeffler Star
 publication/series
 Bachelor’s Theses in Mathematical Sciences
 report number
 LUNFMA40992020
 ISSN
 16546229
 other publication id
 2020:K14
 language
 English
 id
 9024200
 date added to LUP
 20200824 15:08:55
 date last changed
 20200824 15:08:55
@misc{9024200, abstract = {The Swedish mathematician Gösta MittagLeffler (18461927) is wellknown for founding Acta Mathematica, the famous international mathematical journal. His mathematical contributions are connected chiefly with complex analysis. The MittagLeffler 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 wellorganised note of the MittagLeffler 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 MittagLeffler's theorem. Moreover, the concept of the MittagLeffler star, a starshaped open domain will also be defined and proved in detail.}, author = {Liu, Peicen}, issn = {16546229}, keyword = {The MittagLeffler Theorem,Meromorphic Function,Complex Analysis,The MittagLeffler Star}, language = {eng}, note = {Student Paper}, series = {Bachelor’s Theses in Mathematical Sciences}, title = {The Existence of Meromorphic Functions with Prescribed Poles and Principal Parts}, year = {2020}, }