zeta#

Purpose#

Computes the Riemann Zeta function.

f = zeta(z)#

f = zeta(2);

After the above code, f will equal:

1.6449341

which is equivalent to \(\frac{\pi^2}{6}\).

The Riemann zeta function is represented by the equation:

\[\zeta(s) = \frac{1}{\Gamma(s)} \int_0^\infty \frac{x^{s-1}}{e^x-1} dx\]

Euler MacLaurin series.