Find the Fourier' series of $f(t)$, which: $$ f(t)= \begin{cases} \pi^2-t^2 & \text{if} & t\neq 1/\pi^n & n\in \mathbb{N} \\ t^2 &\text{if} & t= 1/\pi^n & n\in \mathbb{N} \end{cases} $$ I tried to make a continuous piecewise function which links the points $t=1/\pi^n\pm \epsilon$ with $t=1/\pi^n$, where $\epsilon$ tends to zero, but the fourier coefficients are kind of large.
I have not found any example of a Fourier' series like this one, so an example would be appreciated.