| Pré. | Proc. |
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