`numpy:i0`

source: /dev/numpy/build-install/usr/lib/python3.14/site-packages/numpy/lib/_function_base_impl.py :3532

Signature

def i0 ( x )

Summary

Modified Bessel function of the first kind, order 0.

Extended Summary

Usually denoted $I_{0}$ .

Parameters

x : array_like of float: Argument of the Bessel function.

Returns

out : ndarray, shape = x.shape, dtype = float: The modified Bessel function evaluated at each of the elements of x.

Notes

The scipy implementation is recommended over this function: it is a proper ufunc written in C, and more than an order of magnitude faster.

We use the algorithm published by Clenshaw ^[1] and referenced by Abramowitz and Stegun ^[2], for which the function domain is partitioned into the two intervals [0,8] and (8,inf), and Chebyshev polynomial expansions are employed in each interval. Relative error on the domain [0,30] using IEEE arithmetic is documented ^[3] as having a peak of 5.8e-16 with an rms of 1.4e-16 (n = 30000).

Examples

import numpy as np

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np.i0(0.)

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np.i0([0, 1, 2, 3])

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Aliases

numpy.i0