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Let $f$ be an entire function with no zeros. Then $f$ must be of the form $f(z)=\exp(g(z))$ where $g$ entire.

Is it true or not? How to prove?

copper.hat
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Shiquan
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  • It's a standard result, available in introductory complex analysis textbooks. Note it can be rephrased: $\log f$ is entire. – Gerry Myerson Feb 16 '14 at 08:23
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    @AlexYoucis I don't believe that reference is a valid duplicate, if only for the scope and OP's apparent perspective (one can't expect freshmen to navigate the accepted answer, although the second should probably be okay). – Jonathan Y. Feb 16 '14 at 08:32
  • To OP: try looking at a primitive of $\frac{g^\prime}{g}$. – Jonathan Y. Feb 16 '14 at 08:43

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