scipy.special.j1#
- scipy.special.j1(x, out=None) = <ufunc 'j1'>#
- Bessel function of the first kind of order 1. - Parameters:
- xarray_like
- Argument (float). 
- outndarray, optional
- Optional output array for the function values 
 
- Returns:
- Jscalar or ndarray
- Value of the Bessel function of the first kind of order 1 at x. 
 
 - See also - jv
- Bessel function of the first kind 
- spherical_jn
- spherical Bessel functions. 
 - Notes - The domain is divided into the intervals [0, 8] and (8, infinity). In the first interval a 24 term Chebyshev expansion is used. 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 - j1. It should not be confused with the spherical Bessel functions (see- spherical_jn).- References [1]- Cephes Mathematical Functions Library, http://www.netlib.org/cephes/ - Examples - Calculate the function at one point: - >>> from scipy.special import j1 >>> j1(1.) 0.44005058574493355 - Calculate the function at several points: - >>> import numpy as np >>> j1(np.array([-2., 0., 4.])) array([-0.57672481, 0. , -0.06604333]) - Plot the function from -20 to 20. - >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots() >>> x = np.linspace(-20., 20., 1000) >>> y = j1(x) >>> ax.plot(x, y) >>> plt.show() 