Hi all,

I have some function $\displaystyle c = e^z + e^{zA} + e^{zA^2}$, $\displaystyle A^3 = 1$ and $\displaystyle A \neq 1$

I know that $\displaystyle e^z = \sum_{n=0}^{\infty}{ \frac{z^n}{ n!} }$

So, $\displaystyle c = \sum_{n=0}^{\infty}{ \frac{z^n}{ n!} } + \sum_{n=0}^{\infty}{ \frac{(zA)^n}{ n!} } + \sum_{n=0}^{\infty}{ \frac{(zA^2)^n}{ n!} }$

$\displaystyle c = \sum_{n=0}^{\infty}{ \frac{(z^n)(1 + A^n + A^{2n})}{ n!} }$

Is this good so far? Can it be simplified further? Thanks a lot.