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

Prove that if a function f:c->c is analytic and lim as z to infinity of f(z)/z = 0 that f is constant.

2. Relevant equations

Cauchy Integral Formula for the first derivative (want to show this is 0 ie: constant)

f prime (z) = 1/(2ipi)*Integral over alpha (circle radius r) f(x)/(x-z)^2 dx.

3. The attempt at a solution

So, I think I'm right in incorporating the cauchy integral formula for the first derivative into my proof. I hope that I can show that the integral over the closed curve is 0 for all z, meaning that 0 is the derivative of f and therefore f is constant.

Problems: Not sure how to show this integral is 0, since using this equation the new integral has a critical point over the point z. I'm assuming that the introduction of the assumption that the limit of f(z)/z = 0 needs to be employed to take care of this.

In other words, I believe I have equiped myself with the right tools, though I'm not sure how to start implamenting them, I'll update the post as I continue working on this problem though any help would be appreciated.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Complex Analysis Proof of Constant Function

**Physics Forums | Science Articles, Homework Help, Discussion**