hermite(n, monic=False)
Defined by
$$H_n(x) = (-1)^ne^{x^2}\frac{d^n}{dx^n}e^{-x^2};$$$H_n$ is a polynomial of degree $n$ .
The polynomials $H_n$ are orthogonal over $(-\infty, \infty)$ with weight function $e^{-x^2}$ .
Degree of the polynomial.
If :None:None:`True`, scale the leading coefficient to be 1. Default is :None:None:`False`.
Hermite polynomial.
Physicist's Hermite polynomial.
>>> 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()
The following pages refer to to this document either explicitly or contain code examples using this.
scipy.special._orthogonal.hermite
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