scipy.special._orthogonal:_roots_hermite_asy

Extended Summary

Computes the sample points and weights for Gauss-Hermite quadrature. The sample points are the roots of the nth degree Hermite polynomial, $H_n(x)$. These sample points and weights correctly integrate polynomials of degree $2n-1$ or less over the interval $[-\infty ,\infty ]$ with weight function $f(x)=e^{-x^2}$.

This method relies on asymptotic expansions which work best for n > 150. The algorithm has linear runtime making computation for very large n feasible.