jnp_zeros#
- 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 - References [1]- Zhang, Shanjie and Jin, Jianming. “Computation of Special Functions”, John Wiley and Sons, 1996, chapter 5. https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html - 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_zerosyields 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 $J_2'$", zorder=5) >>> ax.set_ylim(-0.4, 0.8) >>> ax.set_xlim(0, xmax) >>> plt.legend() >>> plt.show() 