hermite — SciPy v1.15.2 Manual (original) (raw)

scipy.special.

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

Examples

from scipy import special import matplotlib.pyplot as plt import numpy as np

p_monic = special.hermite(3, monic=True) p_monic poly1d([ 1. , 0. , -1.5, 0. ]) p_monic(1) -0.49999999999999983 x = np.linspace(-3, 3, 400) y = p_monic(x) plt.plot(x, y) plt.title("Monic Hermite polynomial of degree 3") plt.xlabel("x") plt.ylabel("H_3(x)") plt.show()