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The constant term of the Fourier coefficients of the periodic function
f(x)={−k,for −pi<x<0k,for 0<x<pi,f(x+2π)=f(x) and k=constantf(x) = \begin{cases} -k, & \text{for } -pi < x < 0 \\ k, & \text{for } 0 < x < pi \end{cases}, \quad f(x + 2\pi) = f(x) \text{ and } k = \text{constant}f(x)={−k,k,for −pi<x<0for 0<x<pi,f(x+2π)=f(x) and k=constant
is
kkk
2k2k2k
2π2\pi2π
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