SciPy

scipy.special.i0

scipy.special.i0(x) = <ufunc 'i0'>

Modified Bessel function of order 0.

Defined as,

\[I_0(x) = \sum_{k=0}^\infty \frac{(x^2/4)^k}{(k!)^2} = J_0(\imath x),\]

where \(J_0\) is the Bessel function of the first kind of order 0.

Parameters:

x : array_like

Argument (float)

Returns:

I : ndarray

Value of the modified Bessel function of order 0 at x.

See also

iv, i0e

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 [R429] routine i0.

References

[R429](1, 2) Cephes Mathematical Functions Library, http://www.netlib.org/cephes/index.html

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