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()