scipy.special.hermitenorm

scipy.special.hermitenorm(n, monic=False)

Normalized (probabilist’s) Hermite polynomial.

Defined by

\[He_n(x) = (-1)^ne^{x^2/2}\frac{d^n}{dx^n}e^{-x^2/2};\]

\(He_n\) is a polynomial of degree \(n\).

Parameters:

n : int

Degree of the polynomial.

monic : bool, optional

If True, scale the leading coefficient to be 1. Default is False.

Returns:

He : orthopoly1d

Hermite polynomial.

Notes

The polynomials \(He_n\) are orthogonal over \((-\infty, \infty)\) with weight function \(e^{-x^2/2}\).