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.

See also

iv: Modified Bessel function of the first kind
i1: Modified Bessel function of order 1

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. i1e is useful for large arguments x: for these, i1 quickly overflows.

References

[1]

Cephes Mathematical Functions Library, http://www.netlib.org/cephes/

Examples

In the following example i1 returns infinity whereas i1e still 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()