I know a lot about the properties of the polynomials, but I don't know for what purpose they were developed or why they continue to be studies.

Why are Orthogonal polynomials important besides their use in Gaussian Quadrature and how are the Hermites particularly interesting?

How did they come to be?

  • 3
    $\begingroup$ en.wikipedia.org/wiki/… , and also (see, for example, Dym and McKean's Fourier analysis book), you can use them as a basis for $L^2(\mathbb{R})$, which diagonalises the Fourier transform. $\endgroup$
    – Chappers
    Apr 29 '15 at 20:17

Hermite polynomials essentially coincide with the eigenfunctions of the most important quantum-mechanical system: the harmonic oscillator.


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