orthax.hermite.hermnorm

orthax.hermite.hermnorm(n)Source

Norm of nth Hermite polynomial.

The norm \(\gamma_n\) is defined such that

\(\int_{-\inf}^{\inf} H_n^2(x) \exp(-x^2) dx = \gamma_n^2\)

With this definition \(\gamma_n^2 = \sqrt{\pi} 2^n n!\)

Parameters:

n (int) – Order of Hermite polynomial.

Returns:

gamma_n (float) – Norm of the nth Hermite polynomial.