scipy.special.y0 — SciPy v1.15.2 Manual (original) (raw)
scipy.special.y0(x, out=None) = <ufunc 'y0'>#
Bessel function of the second kind of order 0.
Parameters:
xarray_like
Argument (float).
outndarray, optional
Optional output array for the function results
Returns:
Yscalar or ndarray
Value of the Bessel function of the second kind of order 0 at x.
See also
Bessel function of the first kind of order 0
Bessel function of the first kind
Notes
The domain is divided into the intervals [0, 5] and (5, infinity). In the first interval a rational approximation \(R(x)\) is employed to compute,
\[Y_0(x) = R(x) + \frac{2 \log(x) J_0(x)}{\pi},\]
where \(J_0\) is the Bessel function of the first kind of order 0.
In the second interval, the Hankel asymptotic expansion is employed with two rational functions of degree 6/6 and 7/7.
This function is a wrapper for the Cephes [1] routine y0.
References
Examples
Calculate the function at one point:
from scipy.special import y0 y0(1.) 0.08825696421567697
Calculate at several points:
import numpy as np y0(np.array([0.5, 2., 3.])) array([-0.44451873, 0.51037567, 0.37685001])
Plot the function from 0 to 10.
import matplotlib.pyplot as plt fig, ax = plt.subplots() x = np.linspace(0., 10., 1000) y = y0(x) ax.plot(x, y) plt.show()
