scipy.special.hermite

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

Physicist’s Hermite polynomial.

Defined by

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

\(H_n\) 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:

H : orthopoly1d

Hermite polynomial.

Notes

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