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Bessel function of order zero.


double x, y, j0();
y = j0(x);


Returns a Bessel function of order zero of the argument. The domain is divided into the intervals [0, 5] and (5, infinity). In the first interval this rational approximation is used:

       2         2
(w - r  ) (w - r  ) P (w) / Q (w)
      1         2    3       8

where w = x  and each r is a zero of the function.

In the second interval, the Hankel asymptotic expansion is employed with two rational functions of degree 6/6 and 7/7.

                      Absolute error:
arithmetic   domain     # trials      peak         rms
    DEC       0, 30       10000       4.4e-17     6.3e-18
    IEEE      0, 30       60000       4.2e-16     1.1e-16