Gibbs phenomenon
Proper noun
Meaning
Gibbs phenomenon
(mathematics) A behaviour of the Fourier series approximation at a jump discontinuity of a piecewise continuously differentiable periodic function, such that partial sums exhibit an oscillation peak adjacent the discontinuity that may overshoot the function maximum (or minimum) itself and does not disappear as more terms are calculated, but rather approaches a finite limit.
Examples
The oscillation seen about the sawtooth when k is large is called the Gibbs phenomenon The trigonometric functions are also important in physics.