The discussion focuses on expanding the function $$cx(x-l)$$ into a Fourier series, specifically into the form $$\sum_{n=-\infty}^{\infty}a_{n}e^{-\alpha_{n} x}$$ where $$\alpha$$ is a constant. Participants noted a potential typo in the original summand, questioning the dependence of the exponential on the index $$n$$. The correct transformation was confirmed to resemble a Fourier series transform, with an example provided: $$cx(x-1) = c\left(\frac{\pi^2}3 + (-2-i)e^{-ix} - (2-i)e^{ix} + ...\right)$$.
PREREQUISITESMathematicians, physicists, and engineers interested in signal analysis, particularly those working with Fourier series and transforms.
Janssens said: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.
Another said:$$cx(x-l)$$ to $$\sum_{n=-\infty}^{\infty}a_{n}e^{-\alpha_{n} x}$$ $\alpha$ is constant any constant