The Riemann zeta function is defined in Abramowitz & Stegun, Section 23.2.
The Riemann zeta function is defined by the infinite sum \(\zeta(s) = \sum_{k=1}^\infty k^{-s}\).
This routine computes the Riemann zeta function \(\zeta(n)\) for integer \(n, n \ne 1\).
This routine computes the Riemann zeta function \(\zeta(s)\) for arbitrary \(s, s \ne 1\).
For large positive argument, the Riemann zeta function approaches one. In this region the fractional part is interesting, and therefore we need a function to evaluate it explicitly.
This routine computes \(\zeta(n) - 1\) for integer \(n, n \ne 1\).
This routine computes \(\zeta(s) - 1\) for arbitrary \(s, s \ne 1.\).