yvp — SciPy v1.15.2 Manual (original) (raw)
scipy.special.
scipy.special.yvp(v, z, n=1)[source]#
Compute derivatives of Bessel functions of the second kind.
Compute the nth derivative of the Bessel function Yv with respect to z.
Parameters:
varray_like of float
Order of Bessel function
zcomplex
Argument at which to evaluate the derivative
nint, default 1
Order of derivative. For 0 returns the BEssel function yv
Returns:
scalar or ndarray
nth derivative of the Bessel function.
See also
Bessel functions of the second kind
Notes
The derivative is computed using the relation DLFM 10.6.7 [2].
References
Examples
Compute the Bessel function of the second kind of order 0 and its first two derivatives at 1.
from scipy.special import yvp yvp(0, 1, 0), yvp(0, 1, 1), yvp(0, 1, 2) (0.088256964215677, 0.7812128213002889, -0.8694697855159659)
Compute the first derivative of the Bessel function of the second kind for several orders at 1 by providing an array for v.
yvp([0, 1, 2], 1, 1) array([0.78121282, 0.86946979, 2.52015239])
Compute the first derivative of the Bessel function of the second kind of order 0 at several points by providing an array for z.
import numpy as np points = np.array([0.5, 1.5, 3.]) yvp(0, points, 1) array([ 1.47147239, 0.41230863, -0.32467442])
Plot the Bessel function of the second kind of order 1 and its first three derivatives.
import matplotlib.pyplot as plt x = np.linspace(0, 5, 1000) x[0] += 1e-15 fig, ax = plt.subplots() ax.plot(x, yvp(1, x, 0), label=r"$Y_1$") ax.plot(x, yvp(1, x, 1), label=r"$Y_1'$") ax.plot(x, yvp(1, x, 2), label=r"$Y_1''$") ax.plot(x, yvp(1, x, 3), label=r"$Y_1'''$") ax.set_ylim(-10, 10) plt.legend() plt.show()
