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