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Math Help - represent this function as power series

  1. #1
    Junior Member
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    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.
    Last edited by director; February 11th 2013 at 07:28 PM.
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  2. #2
    MHF Contributor
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    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.
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