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() 