Dirichlet Conditions (convergence):
If $f(x)$ is extended to be a $2\pi$ periodic function with finitly many jump discontinuities, with
\[ \int_{-\pi}^\pi |f(x)| dx <\infty \] then
$\mm$ (a) the Fourier series converges to $f(x)$ at any continuous point, and
$\mm$ (b) the Fourier series converges to midpoint at any jump.