Help with found Fourier complex series of e^t

[needved]

Homework Statement

i have this function
\begin{equation}
f(t) = e^t
\end{equation}

Homework Equations

[/B]
the Fourier seria have the form
\begin{equation}
f(t) = \sum C_{n} e^{int}
\end{equation}

The Attempt at a Solution

}
[/B]
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 don't have anithing. Any help here please.

thanks in advance

 

[Ray Vickson]

Homework Statement

i have this function
\begin{equation}
f(t) = e^t
\end{equation}

Homework Equations

[/B]
the Fourier seria have the form
\begin{equation}
f(t) = \sum C_{n} e^{int}
\end{equation}

The Attempt at a Solution

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

my attempts are try to find the coeficients doing integration by parts but i don't have anithing. Any help here please.

thanks in advance

(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.