relation between $\zeta(2)$ and the fourier transform of $x^2$ I have problem with see the relation between the transform of $x^2$ in $[-\pi,\pi]$ and the function $\zeta$ de Riemann in the point 2, this say that using the transform fourier of $x^2$ prove that $\zeta (2)$ is equal to $\sum_{n=1}^{\infty}\dfrac{1}{n^2}=\dfrac{\pi^2}{6}$, but here is not my trouble because I did this part but the answer me which is the relation between $\zeta(2)$ the fourier tranform of $x^2$?
After you get the Fourier series for $x^2$  in $[−\pi,\pi]$, put $x=\pi$, and there you go!
After you get the Fourier series for $x^2$  in $[−\pi,\pi]$, put $x=\pi$, and there you go!