scipy.special.i1#
- scipy.special.i1(x, out=None) = <ufunc 'i1'>#
- Modified Bessel function of order 1. - Defined as, \[I_1(x) = \frac{1}{2}x \sum_{k=0}^\infty \frac{(x^2/4)^k}{k! (k + 1)!} = -\imath J_1(\imath x),\]- where \(J_1\) is the Bessel function of the first kind of order 1. - Parameters:
- xarray_like
- Argument (float) 
- outndarray, optional
- Optional output array for the function values 
 
- Returns:
- Iscalar or ndarray
- Value of the modified Bessel function of order 1 at x. 
 
 - See also - Notes - The range is partitioned into the two intervals [0, 8] and (8, infinity). Chebyshev polynomial expansions are employed in each interval. - This function is a wrapper for the Cephes [1] routine - i1.- References [1]- Cephes Mathematical Functions Library, http://www.netlib.org/cephes/ - Examples - Calculate the function at one point: - >>> from scipy.special import i1 >>> i1(1.) 0.5651591039924851 - Calculate the function at several points: - >>> import numpy as np >>> i1(np.array([-2., 0., 6.])) array([-1.59063685, 0. , 61.34193678]) - Plot the function between -10 and 10. - >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots() >>> x = np.linspace(-10., 10., 1000) >>> y = i1(x) >>> ax.plot(x, y) >>> plt.show() 