scipy.special.i1

scipy.special.i1(x, out=None) = <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)

outndarray, optional

Optional output array for the function values

Returns

Iscalar or ndarray

Value of the modified Bessel function of order 1 at x.

See also

iv

i1e

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/