i0(x)
Usually denoted $I_0$ .
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 and referenced by Abramowitz and Stegun , 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 as having a peak of 5.8e-16 with an rms of 1.4e-16 (n = 30000).
Argument of the Bessel function.
The modified Bessel function evaluated at each of the elements of x.
Modified Bessel function of the first kind, order 0.
>>> np.i0(0.) array(1.0)
>>> np.i0([0, 1, 2, 3]) array([1. , 1.26606588, 2.2795853 , 4.88079259])See :
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