Complex Analysis: Entire Function Series

[tarheelborn]

Homework Statement

I need to prove that $$\sum_{n=1}^{∞}[1−Cos(n−1z)]$$ is entire.

Homework Equations

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?

 

[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.

 

[tarheelborn]

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