As a part of a question that I solving about Fourier Series, I had to decide if the Fourier Series in the domain $[-\pi,\pi]$of $\sin(px)$ is uniformly convergent.
Notice that $p>0$ and $p \notin \Bbb Z$. So far I found that:
$$\sin(px)\sim \sum_{n=1}^\infty \frac{(-1)^n2n}{\pi(p^2-n^2)}\sin(\pi p)\sin(\pi x)$$
I don't Understand how to determine if the Series is uniformly convergent to $\sin(px)$. I thought about using Weierstrass M-test but I don't sure how in that case.
Thanks:)