I urgently need help on the following Fourier series expansion:
$f(x) = -1$ on $(-\pi, 0)$ and $f(x) = x$ on $(0, \pi)$.
I would like to find the general formula for the Fourier coefficients, but I have a big problem with that as the function is just so different from all the other ones I have encountered so far as it changes on its domain.