scipy.special.i0#
- scipy.special.i0(x, out=None) = <ufunc 'i0'>#
Modified Bessel function of order 0.
Defined as,
\[I_0(x) = \sum_{k=0}^\infty \frac{(x^2/4)^k}{(k!)^2} = J_0(\imath x),\]where \(J_0\) is the Bessel function of the first kind of order 0.
- 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 0 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
i0
.References
[1]Cephes Mathematical Functions Library, http://www.netlib.org/cephes/
Examples
Calculate the function at one point:
>>> from scipy.special import i0 >>> i0(1.) 1.2660658777520082
Calculate at several points:
>>> import numpy as np >>> i0(np.array([-2., 0., 3.5])) array([2.2795853 , 1. , 7.37820343])
Plot the function from -10 to 10.
>>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots() >>> x = np.linspace(-10., 10., 1000) >>> y = i0(x) >>> ax.plot(x, y) >>> plt.show()