jnp_zeros — SciPy v1.15.3 Manual (original) (raw)

scipy.special.

scipy.special.jnp_zeros(n, nt)[source]#

Compute zeros of integer-order Bessel function derivatives Jn’.

Compute nt zeros of the functions \(J_n'(x)\) on the interval \((0, \infty)\). The zeros are returned in ascending order. Note that this interval excludes the zero at \(x = 0\)that exists for \(n > 1\).

Parameters:

nint

Order of Bessel function

ntint

Number of zeros to return

Returns:

ndarray

First nt zeros of the Bessel function.

See also

jvp

Derivatives of integer-order Bessel functions of the first kind

jv

Float-order Bessel functions of the first kind

References

Examples

Compute the first four roots of \(J_2'\).

from scipy.special import jnp_zeros jnp_zeros(2, 4) array([ 3.05423693, 6.70613319, 9.96946782, 13.17037086])

As jnp_zeros yields the roots of \(J_n'\), it can be used to compute the locations of the peaks of \(J_n\). Plot\(J_2\), \(J_2'\) and the locations of the roots of \(J_2'\).

import numpy as np import matplotlib.pyplot as plt from scipy.special import jn, jnp_zeros, jvp j2_roots = jnp_zeros(2, 4) xmax = 15 x = np.linspace(0, xmax, 500) fig, ax = plt.subplots() ax.plot(x, jn(2, x), label=r'$J_2$') ax.plot(x, jvp(2, x, 1), label=r"$J_2'$") ax.hlines(0, 0, xmax, color='k') ax.scatter(j2_roots, np.zeros((4, )), s=30, c='r', ... label=r"Roots of J2′J_2'J2′​", zorder=5) ax.set_ylim(-0.4, 0.8) ax.set_xlim(0, xmax) plt.legend() plt.show()