Study the Oscillations Created by n^th Derivatives

This example shows how the higher derivatives of a function generate oscillations. The oscillations occupy larger intervals of the real line as the order of the derivatives increases.

Find the ^th derivative of a Gaussian exponential function.

This closed-form can also be expressed in terms of Hermite polynomials.

The higher derivatives of the Gaussian function generate oscillations as shown in the following.

These derivatives are used for preparing Gaussian filters in image processing.