Series Representations of Analytic Functions Defined In the Complex Plane

Kanee Goodfaith Leyira¹

Section:Research Paper, Product Type: Journal-Paper
Vol.9 , Issue.4 , pp.53-58, Aug-2022

Online published on Aug 31, 2022

Copyright © Kanee Goodfaith Leyira . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
In this study, we examine the Taylor and Laurent Series for Series Representations of Analytic Functions as Defined in the Complex Plane. We explained the methodology following the statement of some series, theorems, convergences and their proofs applying the Cauchy’s integral formula and Weierstrass M-Test. The results of the study are discussed through solving some examples. The study concludes that analytic functions as a power series brings us to Taylor and Laurent series as defined in the complex plane.

Key-Words / Index Term :
Analytic Function, Complex Plane, Convergences, Power Series, Singularity.

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