$f_n:\Omega\ -> C$ analytics with $\Omega$ open subset of $C$, converges uniformly to $f$ on every K compact subset of $\Omega$
I tried working with the definition of uniform convergence but got nowhere.
2026-04-07 02:09:23.1775527763
Prove that if $f_n$ analitics converges uniformly to $f$ then $f_n^{'}$ converges uniformly to $f^{'}$
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Hint: Cauchy integral formula expresses $f'(a)$ in terms of an integral involving $f$ around a curve.