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Published in:
2017 | OriginalPaper | Chapter
Proof of Theorem 11.9. Power Series (Continued). Taylor Series. Local Power Series Expansion of a Holomorphic Function. Cauchy’s Inequalities. The Uniqueness Theorem
Author : Alexander Isaev
Published in: Twenty-One Lectures on Complex Analysis
Publisher: Springer International Publishing
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Clearly, a power series centred at a converges on its disk of convergence $$ \varDelta(a,R) $$ and diverges at every point z satisfying $$ |z-a|>R.\ \mathrm{For}\neq0, \infty $$ it is therefore natural to investigate convergence properties of the series at the points of the circle $$ \{z \in \mathbb{C} : |z-a| =R \} $$ , which is the boundary $$ \partial \varDelta (a,R) $$ of the disk of convergence.