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() 