The Dirichlet Kernel $$D_N =\frac{\sin(N+1/2)x}{\sin x/2}$$ How to show this $$\frac{1}{2\pi}\int_{\pi}^{\pi}|D_N|dx=\frac{4}{\pi^2}\log N+O(1)$$
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It is found on the Stein's Fourier Analysis,Page 66 – Alexander Lau Oct 28 '18 at 13:07
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See for example here, here or here – Delta-u Oct 28 '18 at 13:09
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Thank you ,it's a great help ! – Alexander Lau Oct 28 '18 at 13:12