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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 $e^{-x^2/2}$.