# represent this function as power series

• February 11th 2013, 07:49 PM
director
represent this function as power series
Hi all,

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

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

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

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

Is this good so far? Can it be simplified further? Thanks a lot.
• February 11th 2013, 10:16 PM
chiro
Re: represent this function as power series
Hey director.

That looks good and is in power series form so I don't think you can go any further.