scipy.special.
yn_zeros#
- scipy.special.yn_zeros(n, nt)[source]#
Compute zeros of integer-order Bessel function Yn(x).
Compute nt zeros of the functions \(Y_n(x)\) on the interval \((0, \infty)\). The zeros are returned in ascending order.
- 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 \(Y_2\).
>>> from scipy.special import yn_zeros >>> yn_zeros(2, 4) array([ 3.38424177, 6.79380751, 10.02347798, 13.20998671])
Plot \(Y_2\) and its first four roots.
>>> import numpy as np >>> import matplotlib.pyplot as plt >>> from scipy.special import yn, yn_zeros >>> xmin = 2 >>> xmax = 15 >>> x = np.linspace(xmin, xmax, 500) >>> fig, ax = plt.subplots() >>> ax.hlines(0, xmin, xmax, color='k') >>> ax.plot(x, yn(2, x), label=r'$Y_2$') >>> ax.scatter(yn_zeros(2, 4), np.zeros((4, )), s=30, c='r', ... label='Roots', zorder=5) >>> ax.set_ylim(-0.4, 0.4) >>> ax.set_xlim(xmin, xmax) >>> plt.legend() >>> plt.show()