ZETA _ _ _ _ _ _ _ _ _ _ _ _ operator

The Zeta operator returns Riemann's Zeta function,

Zeta (z) := sum(1/(k**z),k,1,infinity)

syntax:

examples:

Zeta(2); 

    2
  pi  / 6 


on rounded; 

Zeta 1.01; 

  100.577943338

Numerical computation for the Zeta function for arguments close to 1 are tedious, because the series is converging very slowly. In this case a formula (e.g. found in Bender/Orzag: Advanced Mathematical Methods for Scientists and Engineers, McGraw-Hill) is used.

No numerical approximation for complex arguments is done.