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

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 \(e^{-x^2/2}\).