Analytic Function
Posted: Tue Jul 12, 2016 7:35 am
If \( f(z) \) is analytic and represented by a locally convergent power series , is \( f(\bar{z}) \) analytic too?
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.