the series E k converges uniformly on D(0;r) for every r E (0,1), but diverges on C\ D(0; 1). More generally, let f:D(0; 1) → C be a holomorphic function with f(0) = 0. Show that k=1 converges uniformly on D(0; r) for every r E (0,1). Hint: f(z)/z can be extended to become a continuous function on D(0; r). Why?

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