I need a reference that explains the following result (also known as the Gibbs phenomenon)
Let $g$ be a $2\pi$-periodic function, $C^1$ per pieces (i.e., there exists a partition $x_1 < \cdots < x_n$ such that $g$ is $C^1$ in $[x_i,x_{i+1}]$) and suppose that $g$ is discontinuous on $x_i \forall i=1,\ldots,n$.
If $S_n(x)$ is the $n$'th Fourier partial sum of $g$ and $\delta_{i,n}=x_i+\frac{\pi}{n+1}$, we have:
$\lim_{n\to\infty} S_n(\delta_{i,n})=\frac{1}{2}(g(x_i+0)+g(x_i-0))+\frac{\nu}{\pi}(g(x_i+0)+g(x_i-0))$, where $g(x_i+0)$ is the right limit of $g$ in $x_i$ (analogous for $g(x_i-0)$) and $\nu = \int_{0}^{\pi} \frac{\sin(t)}{t} dt$.
Thank you in advance!