The H(n, x) function computes the nth Hermite polynomial evaluated at x.

The Hermite polynomials are orthogonal on the interval ($-\mathrm{\infty },\mathrm{\infty }$) with respect to the weight function $w\left(x\right)={\ⅇ}^{-x^2}$. They satisfy:

Hermite polynomials satisfy the following recurrence relation:

$\mathrm{with}\left(\mathrm{orthopoly}\right)\:$

$H\left(2\,x\right)$

$4x^2-2$

$H\left(3\,x\right)$

$8x^3-12x$

$H\left(10\,5\right)$

$3275529760$