I am given the following function: $f(x) = ( \pi + x) $ , $ -\pi \leq x \leq \pi $
I need to find the Fourier series of the function as well as the pointwise sum of the series and the graph of the sum of the series to check for uniform convergence (if there is any).
I calculated the Fourier series:
$ f(x) \sim \pi + \sum\limits_{k=1}^{\infty} \frac{-2(-1)^k\sin(kx)} {k} $
I needed to ask if pointwise sum of this function would be equal to its general sum which we can get by substituting $x = 0$
Also, how can we identify the point of convergence using the graph?