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Help with found Fourier complex series of e^t

  1. Feb 28, 2017 #1
    1. The problem statement, all variables and given/known data
    i have this function
    \begin{equation}
    f(t) = e^t
    \end{equation}

    2. Relevant equations

    the fourier seria have the form
    \begin{equation}
    f(t) = \sum C_{n} e^{int}
    \end{equation}


    3. The attempt at a solution}

    so i need to find the coeficients $c_{n}$ given by
    \begin{equation}
    \frac{1}{2\pi} \int_{-\pi}^{\pi} f(t) e^{int} dt
    \end{equation}

    my attempts are try to find the coeficients doing integration by parts but i dont have anithing. Any help here please.

    thanks in advance
     
    Last edited: Feb 28, 2017
  2. jcsd
  3. Feb 28, 2017 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    (1)What is the interval over which you want the Fourier series? The series produces a periodic function of ##t##, but ##e^t## is not periodic on the whole line.
    (2) You have an elementary integral that you ought to be able to solve almost by inspection. No fancy integration tools are needed, and certainly integration by parts is overkill.
     
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