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y0

Bessel function of the second kind, order zero, of the argument.

SYNOPSIS:

double x, y, y0();
y = y0(x);

DESCRIPTION:

Returns a Bessel function of the second kind, of order zero, of the argument.
The domain is divided into the intervals [0, 5] and (5, infinity). In the first interval a rational approximation R(x) is employed to compute:

   y0(x)  = R(x)  +   2 * log(x) * j0(x) / PI.

Thus a call to j0() is required.

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

ACCURACY:

Absolute error, when y0(x) < 1; else relative error:

arithmetic   domain     # trials      peak         rms
    DEC       0, 30        9400       7.0e-17     7.9e-18
    IEEE      0, 30       30000       1.3e-15     1.6e-16