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August 22nd, 2016, 11:34 AM   #1
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Analytic Continuation

Any guidance with this problem would be much appreciated:

Let f(z) be an analytic function defined in a disk |z|<r. Show that the functional equation f(2z)=f(z)f'(z) satisfied on |z|<r/2 implies that f(z) is an entire function.
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