k0

Modified Bessel function, third kind, order zero.

SYNOPSIS:

double x, y, k0();
y = k0(x);

DESCRIPTION:

Returns the modified Bessel function of the third kind of order zero of the argument.
The range is partitioned into the two intervals [0,8] and (8, infinity). Chebyshev polynomial expansions are employed in each interval.

ACCURACY:

Tested at 2000 random points between 0 and 8. Peak absolute error (relative when K0 > 1) was 1.46e-14; rms, 4.26e-15.

Relative error:
arithmetic domain # trials peak rms
DEC 0, 30 3100 1.3e-16 2.1e-17
IEEE 0, 30 30000 1.2e-15 1.6e-16

ERROR MESSAGES:

message condition value returned
domain x <= 0 MAXNUM