In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence.

The polynomials arise in:

probability, such as the Edgeworth series;
✅in combinatorics, as an example of an Appell sequence, obeying the umbral calculus;
✅in numerical analysis as Gaussian quadrature;
✅in physics, where they give rise to the eigenstates of the quantum harmonic oscillator;
✅in systems theory in connection with nonlinear operations on Gaussian noise.
✅in random matrix theory in Wigner–Dyson ensembles.

Here’s a Quick note on Hermite Polynomial and Hermite Functions. This is pretty much what you will need for your competitive exams and interviews.