Analytic Function

Complex Analysis
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Tolaso J Kos
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Analytic Function

#1

Post by Tolaso J Kos »

If \( f(z) \) is analytic and represented by a locally convergent power series , is \( f(\bar{z}) \) analytic too?
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Demetres
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Re: Analytic Function

#2

Post by Demetres »

No it is not. For example \(z\) is analytic but \(\overline{z}\) is not. (As can be checked e.g. by the Cauchy-Riemann equations.)

By the way, "analytic" and "locally represented by a convergent power series" mean the same thing.
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