# 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.

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

References



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()
```