Gibbs Phenomenon

Introduced in MATH213 when learning about Fourier Series.

Gibbs Phenomenon

For a $L^2([a,b])$ function $f$ with periodic extension $f_p$, if $f_p$ is not continuous at some point $t_0$ then truncated Fourier series of $f$ will have growing oscillations near the point $t_0$. This is called Gibbs Phenomenon.

These oscillations do not appear in the infinite sum.