SciPy

scipy.special.hermite

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

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
nint

Degree of the polynomial.

monicbool, optional

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

Returns
Horthopoly1d

Hermite polynomial.

Notes

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

Previous topic

scipy.special.genlaguerre

Next topic

scipy.special.hermitenorm