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