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<tex dpi="150">\Phi_n=\frac{1}{2\pi(n+1)}(\frac{\sin{(\frac{n+1}{2})t}}{\sin{\frac{t}{2}}})^2</tex>
|proof=
<tex dpi="150">\Phi_n(t)=\frac{1}{n+1}\sum\limits_{k=0}^{n}\frac{1}{2\pi}\frac{\sin{(k+\frac{1}{2})t}}{\sin{\frac{t}{2}}}=\frac{1}{2\pi(n+1)}\frac{1}{\sin{\frac{t}{2}}}\sum\limits_{k=0}^{n}(\sin{((k+\frac{1}{2})t)}t\sin{\frac{t}{2}})=</tex>
<tex dpi="150"> \frac{1}{2\pi(n+1)}\frac{1}{\sin{\frac{t}{2}}}\sum\limits_{k=0}^{n}\frac{1}{2}(\cos{kt}-\cos{(k+1)t})=\frac{1}{2\pi(n+1)}\frac{1-\cos{(n+1)t}}{2\sin^2{\frac{t}{2}}}=\frac{1}{2\pi(n+1)}\frac{\sin^2{\frac{n+1}{2}t}}{\sin^2{\frac{t}{2}}}</tex>
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