# scipy.special.i1¶

scipy.special.i1(x) = <ufunc 'i1'>

Modified Bessel function of order 1.

Defined as,

$I_1(x) = \frac{1}{2}x \sum_{k=0}^\infty \frac{(x^2/4)^k}{k! (k + 1)!} = -\imath J_1(\imath x),$

where $$J_1$$ is the Bessel function of the first kind of order 1.

Parameters
xarray_like

Argument (float)

Returns
Indarray

Value of the 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.

This function is a wrapper for the Cephes [1] routine i1.

References

1

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

#### Previous topic

scipy.special.i0e

#### Next topic

scipy.special.i1e