If Fourier series of $ x(t)=\alpha_k$ then what is the Fourier series of $ x^2(t)$?
I should solve this problem and I do not know where to start. I know this is not a question and it is vague but Thanks in advance for your help
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I think that it seems like x(t) is constant, in which case, $x^2(t)$ would also be constant and have fourier series $a_k^2$, although I may very well be wrong. – BelowAverageIntelligence May 02 '18 at 18:28
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@BelowAverageIntelligence thanks for your reply. – Moeen Tabrizi May 02 '18 at 19:09
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Hint: $$\left (\sum_{k=-\infty}^\infty a_k e^{i k x}\right)^2=\sum_{k=-\infty}^\infty c_k e^{i k x}\Rightarrow c_k=\sum_{l=-\infty}^\infty a_l a_{k-l}.$$
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