scipy.special.y1#
- scipy.special.y1(x, out=None) = <ufunc 'y1'>#
Bessel function of the second kind of order 1.
- 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 1 at x.
See also
Notes
The domain is divided into the intervals [0, 8] and (8, infinity). In the first interval a 25 term Chebyshev expansion is used, and computing \(J_1\) (the Bessel function of the first kind) is required. In the second, the asymptotic trigonometric representation is employed using two rational functions of degree 5/5.
This function is a wrapper for the Cephes [1] routine
y1
.References
[1]Cephes Mathematical Functions Library, http://www.netlib.org/cephes/
Examples
Calculate the function at one point:
>>> from scipy.special import y1 >>> y1(1.) -0.7812128213002888
Calculate at several points:
>>> import numpy as np >>> y1(np.array([0.5, 2., 3.])) array([-1.47147239, -0.10703243, 0.32467442])
Plot the function from 0 to 10.
>>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots() >>> x = np.linspace(0., 10., 1000) >>> y = y1(x) >>> ax.plot(x, y) >>> plt.show()