scipy.special.i1e#
- scipy.special.i1e(x, out=None) = <ufunc 'i1e'>#
- Exponentially scaled modified Bessel function of order 1. - Defined as: - i1e(x) = exp(-abs(x)) * i1(x) - Parameters:
- xarray_like
- Argument (float) 
- outndarray, optional
- Optional output array for the function values 
 
- Returns:
- Iscalar or ndarray
- Value of the exponentially scaled modified Bessel function of order 1 at x. 
 
 - Notes - The range is partitioned into the two intervals [0, 8] and (8, infinity). Chebyshev polynomial expansions are employed in each interval. The polynomial expansions used are the same as those in - i1, but they are not multiplied by the dominant exponential factor.- This function is a wrapper for the Cephes [1] routine - i1e.- i1eis useful for large arguments x: for these,- i1quickly overflows.- References [1]- Cephes Mathematical Functions Library, http://www.netlib.org/cephes/ - Examples - In the following example - i1returns infinity whereas- i1estill returns a finite number.- >>> from scipy.special import i1, i1e >>> i1(1000.), i1e(1000.) (inf, 0.01261093025692863) - Calculate the function at several points by providing a NumPy array or list for x: - >>> import numpy as np >>> i1e(np.array([-2., 0., 6.])) array([-0.21526929, 0. , 0.15205146]) - Plot the function between -10 and 10. - >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots() >>> x = np.linspace(-10., 10., 1000) >>> y = i1e(x) >>> ax.plot(x, y) >>> plt.show() 