Question

value of Hermite's polynomial​

Answer 1

Answer:

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.