(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If f(z) is an entire function such that f(z)/z is bounded for |z|>R, then f''(z_0) = 0 for all z_0.

2. Relevant equations

Liouville's theorem

Cauchy estimates: Suppose f is analytic for |z-z_0| ≤ ρ. If |f(z)|≤ M for |z-z_0| = ρ then the mth derivative of f at z_0 is bounded by a constant given in the book.

3. The attempt at a solution

I'm supposed to adapt the proof of Liouville's theorem I learned, which is by using the Cauchy estimates.

I don't see where to get the second derivative of f. I'm pretty sure that z/f(z) is bounded for |z|<1/R, and I tried using the Cauchy estimates but couldn't get anything.

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# Homework Help: Liouville-type problem (Complex analysis)

Can you offer guidance or do you also need help?

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