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

AI Thread Summary
The function cx(x-l) is proposed for expansion into a Fourier series of the form Σ a_n e^(-α_n x). There is confusion regarding the term α, with suggestions that it should depend on n for proper Fourier series representation. The discussion indicates that cx(x-l) can be transformed into a series involving complex exponentials. A specific example is provided, showing a potential expansion with constants and exponential terms. The conversation highlights the need for clarity in defining parameters for accurate series representation.
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I have a function $$cx(x-l)$$ where c is constant

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

how can i do it? you have a idea
 
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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.
 
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.


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

That looks like a Fourier series transform.

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