`scipy.special._orthogonal:hermite`

Signature

def hermite(n, monic = False)

Physicist's Hermite polynomial.

Defined by

H_{n} (x) = (- 1)^{n} e^{x^{2}} \frac{d ^{n}}{d x ^{n}} e^{- x^{2}};

$H_{n}$ is a polynomial of degree $n$ .

n : int: Degree of the polynomial.
monic : bool, optional: If True, scale the leading coefficient to be 1. Default is False.

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

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)

✗

np.float64(-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)")

✗

Text(0, 0.5, 'H_3(x)')

plt.show()

✓