I have a function with period $T = 2\pi$ defined as
$f(x) = x + 3 \quad\textrm{if}\quad 0\leq x<2\pi$
I calculated the Fourier series at points $x\neq 0 + kT$
$f(x)=\pi+3+\sum_{n=1}^{\infty}-\frac{2}{n}sin(nx)$
Now they ask me to find the Fourier series at points $x=0 + kT$
What I did is I know the Fourier series converges to $\frac{1}{2}[f(x<0+kT)+f(x>0+kT)]$, which in this case is $\pi + 3$ so is it correct to say that the Fourier series at the points of discontinuity is $f(x) = \pi+3$?