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Fourier Analysis

Exact result

-2 e^(-i x) - 2 e^(i x) + 1/2 e^(-2 i x) + 1/2 e^(2 i x) - 2/9 e^(-3 i x) - 2/9 e^(3 i x) + π^2/3

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Alternate forms

-4 cos(x) + cos(2 x) - 4/9 cos(3 x) + π^2/3

1/18 (-36 e^(-i x) - 36 e^(i x) + 9 e^(-2 i x) + 9 e^(2 i x) - 4 e^(-3 i x) - 4 e^(3 i x) + 6 π^2)

-1/18 e^(-3 i x) (-9 e^(i x) + 36 e^(2 i x) + 36 e^(4 i x) - 9 e^(5 i x) + 4 e^(6 i x) - 6 π^2 e^(3 i x) + 4)