"Compute the Fourier series of the periodic function $f(x)$ that is defined in $\mathbb R$ as follows:
$$f(x) = |x-2n \pi| $$ for all $x$ s.t. $(2n-1)\pi < x <(2n + 1)\pi.$
Give the definition of a tempered regular distribution, and explain why $f(x)$ is such a distribution. Finally compute the 2nd distributional derivative of $f(x)$."
I am stuck on the first one in finding the Fourier series.
I have problem finding the coefficient in front of the cosine, (the integral), assuming n is real I end up with:
integral from (2n-1)*pi to (2n+1)*pi of |x-2n*pi| cos(kx) dx