In this section we will analyze the Fourier coefficients of $\mathrm{Maj}_n$. In fact, we give an explicit formula for them in Theorem 16 below. But most of the time this formula is not too useful; instead, it’s better to understand the Fourier coefficients of $\mathrm{Maj}_n$ asymptotically as $n \to \infty$.

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Ryan O'Donnell: Yes, thanks! Sorry for the delay in replying.Ryan O'Donnell: No, it's definitely messed up. Will fix!Ryan O'Donnell: Thanks!Ryan O'Donnell: Hi Amir. It's just a 'dummy variable'; in some sense an X's...Ryan O'Donnell: Right, or I guess I can just switch 'codimension' to 'dimens...Ryan O'Donnell: Yep, thanks!Ryan O'Donnell: Thanks, seems like I spotted this one myself too. (Not corr...