How to Expand cx(x-l) into a Fourier Series?

[Another1]

I have a function \(\displaystyle cx(x-l)\) where c is constant

I want to expansion this function \(\displaystyle cx(x-l)\) to \(\displaystyle \sum_{n=-\infty}^{\infty}a_{n}e^{-\alpha x}\)

how can i do it? you have a idea

 

[S.G. Janssens]

Is there perhaps a typo in the summand? The exponential does not seem to depend on $n$ and it is not clear to me what $\alpha$ is.

 

[Another1]

Is there perhaps a typo in the summand? The exponential does not seem to depend on $n$ and it is not clear to me what $\alpha$ is.

\(\displaystyle cx(x-l)\) to \(\displaystyle \sum_{n=-\infty}^{\infty}a_{n}e^{-\alpha_{n} x}\) $\alpha$ is constant any constant

 

[I like Serena]

\(\displaystyle cx(x-l)\) to \(\displaystyle \sum_{n=-\infty}^{\infty}a_{n}e^{-\alpha_{n} x}\) $\alpha$ is constant any constant

That looks like a Fourier series transform.

We have:
$$cx(x-1) = c\left(\frac{\pi^2}3 + (-2-i)e^{-ix} - (2-i)e^{ix} + ...\right)$$