I am calculating the Fourier series of odd and even extensions of various functions e.g. $cos(x),x^2,e^x$ etc.
I need to state whether each series converges uniformly or not, I am struggling to grasp what actually does uniform convergence mean without having to prove it rigorously.
For example I found that the Fourier series for an odd extension of $cos(x)$ over $[-\pi,\pi]$ to be the infinite sum:
$f_1(x) = \frac{2}{\pi}[\frac{4}{3}sin(2x)+\frac{8}{15}sin(4x) + ...+\frac{2*(2k)}{(2k)^2-1}sin(2kx)+...]$
How would I immediately know or be able to check whether this series converges uniformly?