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Hermite polynomials
Polynomial sequence
Hermite polynomials
In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence. The polynomials arise in: signal processing as Hermitian wavelets for wavelet transform analysis probability, such as the Edgeworth series, as well as in connection with Brownian motion; combinatorics, as an example of an Appell sequence, obeying the umbral calculus; numerical analysis as Gaussian quadrature; physics, where they give rise to the eigenstates of the quantum harmonic oscillator; and they also occur in some cases of the heat equation (when the term x u x {\displaystyle {\begin{aligned}xu_{x}\end{aligned}}} is present); systems theory in connection with nonlinear operations on Gaussian noise. random matrix theory in Gaussian ensembles...
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