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