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Unformatted text preview: D, z 6 = 0. Let f ( z ) = a + a 1 z + a 2 z 2 + ... in a neighborhood of 0. Prove the equality z = lim n a n a n +1 . 6. Let f be a holomorphic function in the unit disc D . a) Prove that if f is unjective in D then f ( z ) 6 = 0 for all z D . b) Show that the converse is not true: there is a holomorphic function f in D whose derivative has no zeros in D but f is not injective in D ....
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- Spring '09