SciPy

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:

x : array_like

Argument (float)

Returns:

I : 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 [R431] routine i1.

References

[R431](1, 2) Cephes Mathematical Functions Library, http://www.netlib.org/cephes/index.html

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