THE TEYLOR SERIES AND THEIR PROPERTIES
Keywords:
Taylor series, convergent series, absolute convergence, Weierstrass criterion, Abel's theorem, Cauchy-Adamard formula, holomorphic function.Abstract
This article examines Taylor series and their properties. Mainly, basic concepts related to convergence, such as the radius of convergence of power series, Abel's theorem, Cauchy-Adamard formula are analyzed. The uniqueness of the Taylor series, the methods of expanding functions into a Taylor series, and the properties of holomorphic functions are shown. The absolute and uniform convergence of series, the Cauchy inequality, and their significance in complex analysis are discussed. The article also examines the applications of Taylor series in mathematical analysis and complex analysis.
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