`scipy.special._basic:y1_zeros`

source: /scipy/special/_basic.py :648

Signature

def y1_zeros ( nt , complex = False )

Summary

Compute nt zeros of Bessel function Y1(z), and derivative at each zero.

Extended Summary

The derivatives are given by Y1'(z1) = Y0(z1) at each zero z1.

Parameters

nt : int: Number of zeros to return
complex : bool, default False: Set to False to return only the real zeros; set to True to return only the complex zeros with negative real part and positive imaginary part. Note that the complex conjugates of the latter are also zeros of the function, but are not returned by this routine.

Returns

z1n : ndarray: Location of nth zero of Y1(z)
y1pz1n : ndarray: Value of derivative Y1'(z1) for nth zero

Examples

Compute the first 4 real roots and the derivatives at the roots of :math:`Y_1`:

import numpy as np
from scipy.special import y1_zeros
zeros, grads = y1_zeros(4)
with np.printoptions(precision=5):
    print(f"Roots: {zeros}")
    print(f"Gradients: {grads}")

✓

Extract the real parts:

realzeros = zeros.real

✓

realzeros

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Plot :math:`Y_1` and the first four computed roots.

import matplotlib.pyplot as plt
from scipy.special import y1
xmin = 0
xmax = 13
x = np.linspace(xmin, xmax, 500)
zeros, grads = y1_zeros(4)
fig, ax = plt.subplots()

✓

ax.hlines(0, xmin, xmax, color='k')
ax.plot(x, y1(x), label=r'$Y_1$')
ax.scatter(zeros.real, np.zeros((4, )), s=30, c='r',
           label=r'$Y_1$_zeros', zorder=5)
ax.set_ylim(-0.5, 0.5)
ax.set_xlim(xmin, xmax)
plt.legend()

✗

plt.show()

✓

Compute the first 4 complex roots and the derivatives at the roots of :math:`Y_1` by setting ``complex=True``:

y1_zeros(4, True)

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Aliases

scipy.special.y1_zeros