Modified Bessel function of the first kind, order 0.
Usually denoted \(I_0\).
- xarray_like of float
Argument of the Bessel function.
- outndarray, shape = x.shape, dtype = float
The modified Bessel function evaluated at each of the elements of x.
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).
C. W. Clenshaw, “Chebyshev series for mathematical functions”, in National Physical Laboratory Mathematical Tables, vol. 5, London: Her Majesty’s Stationery Office, 1962.
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, 10th printing, New York: Dover, 1964, pp. 379. http://www.math.sfu.ca/~cbm/aands/page_379.htm
>>> np.i0(0.) array(1.0) >>> np.i0([0, 1, 2, 3]) array([1. , 1.26606588, 2.2795853 , 4.88079259])