Chapter 1 Fourier Series
... |Sk (t) − f (t)| < for every k > N (, t)|. Then the finite sum trigonometric
polynomial Sk (t) will approximate f (t) with an error < . However, in
general N depends on the point t; we have to recompute it for each t. What
we would prefer is uniform convergence. The Fourier series of f will conv ...