Complex Analysis 11 | Power Series Are Holomorphic - Proof [dark version]

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This is my video series about Complex Analysis. I hope that it will help everyone who wants to learn about complex derivatives, curve integrals, and the residue theorem. Complex Analysis has a lof applications in other parts of mathematics and in physics.

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00:00 Intro
00:21 Recap: results for power series
1:52 Proof of the first result (convergence of a k-power series)
6:50 Proof of the second result (convergence of a k-1-power series)
8:46 Proof of the third result (complex differentiability)

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(This explanation fits to lectures for students in their first or second year of study: Mathematics, Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)