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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 $e^{-x^2}$.