zetac

Riemann zeta function.

SYNOPSIS:
double x, y, zetac();
y = zetac(x);

DESCRIPTION:
inf.
- -x
zetac(x) = > k , x > 1,
-
k=2

Is related to the Riemann zeta function by:

Riemann zeta(x) = zetac(x) + 1.

Extension of the function definition for x < 1 is implemented.
Zero is returned for x > log2(MAXNUM).

An overflow error might occur for large negative x, due to the gamma function in the reflection formula.

ACCURACY:
Tabulated values have full machine accuracy.

Relative error:
arithmetic domain # trials peak rms
IEEE 1,50 10000 9.8e-16 1.3e-16
DEC 1,50 2000 1.1e-16 1.9e-17