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 finite element methods as shape functions for beams; 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.