Calculating Fourier Series of $ x^2 (t)$

Question

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

Answer 1

Hint: $$\left (\sum_{k=-\infty}^\infty a_k e^{i k x}\right)^2=\sum_{k=-\infty}^\infty c_k e^{i k x}\Rightarrow c_k=\sum_{l=-\infty}^\infty a_l a_{k-l}.$$