scipy.special.hermitenorm

scipy.special.hermitenorm(n, monic=False)[source]

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
nint

Degree of the polynomial.

monicbool, optional

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

Returns
Heorthopoly1d

Hermite polynomial.

Notes

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