scipy.special.y0#
- 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.
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
[1]Cephes Mathematical Functions Library, http://www.netlib.org/cephes/
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()