jax.scipy.special.i1

jax.scipy.special.i1(x)[source]

Modified Bessel function of order 1.

LAX-backend implementation of i1(). Original docstring below.

i1(x, /, out=None, *, where=True, casting=’same_kind’, order=’K’, dtype=None, subok=True[, signature, extobj])

i1(x)

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

x (array_like) – Argument (float)

Returns

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

Return type

ndarray

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.

See also

iv(), i1e()

References

1

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