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

yn: Bessel function of the second kind for integer order
yv: Bessel function of the second kind for real order

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()

../../_images/scipy-special-yn_zeros-1.png