# Complex Analysis: Entire Function Series

1. Feb 16, 2012

### tarheelborn

1. The problem statement, all variables and given/known data
I need to prove that $$\sum_{n=1}^{∞}[1−Cos(n−1z)]$$ is entire.

2. Relevant equations

3. The attempt at a solution
I know that I need to show that the series is differentiable for its whole domain, but I am not sure how to do that. Should I try to use the ratio test?

2. Feb 16, 2012

### Dick

You probably mean 1-cos(z/n). Yes, expand the cos in a power series and try to say something about the convergence of the summed series using the ratio test.

3. Feb 17, 2012

### tarheelborn

Oops, that is what I mean. Thank you very much.