Gibbs phenomenon

A fixed-size overshoot that a Fourier partial sum makes right next to a jump discontinuity, no matter how many terms are added.

The Gibbs phenomenon is the persistent overshoot -- about 9% of the jump's size -- that a Fourier series' partial sums make just to either side of a jump discontinuity; adding more terms narrows the overshoot's width toward the jump but never shrinks its height, unlike the pointwise error away from the jump, which does shrink to zero.