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Zeta

Zeta[s]
gives the Riemann zeta function zeta(s).
Zeta[s, a]
gives the generalized Riemann zeta function zeta(s,a).
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • For Re(s)>1, zeta(s)=∑_(k=1)^∞k^(-s).
  • zeta(s,a)=∑_(k=0)^(∞)(k+a)^(-s), where any term with k+a=0 is excluded.
  • For Re(a)<0, the definition used is zeta(s,a)=∑_(k=0)^(∞)((k+a)^2)^(-s/2).
  • Zeta[s] has no branch cut discontinuities.
  • For certain special arguments, Zeta automatically evaluates to exact values.
  • Zeta can be evaluated to arbitrary numerical precision.
  • Zeta automatically threads over lists.
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