numpy.i0(x)
[source]
Modified Bessel function of the first kind, order 0.
Usually denoted . This function does broadcast, but will not “up-cast” int dtype arguments unless accompanied by at least one float or complex dtype argument (see Raises below).
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See also
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).
[1] | C. W. Clenshaw, “Chebyshev series for mathematical functions”, in National Physical Laboratory Mathematical Tables, vol. 5, London: Her Majesty’s Stationery Office, 1962. |
[2] | 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 |
[3] | http://kobesearch.cpan.org/htdocs/Math-Cephes/Math/Cephes.html |
>>> np.i0(0.) array(1.0) # may vary >>> np.i0([0., 1. + 2j]) array([ 1.00000000+0.j , 0.18785373+0.64616944j]) # may vary
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https://docs.scipy.org/doc/numpy-1.17.0/reference/generated/numpy.i0.html