Wolfram Mathematica Documentation Center
DOCUMENTATION CENTER SEARCH
Mathematica > Mathematics and Algorithms > Mathematical Functions > Special Functions > Zeta Functions & Polylogarithms >
Mathematica > Mathematics and Algorithms > Number Theory > Analytic Number Theory > Zeta Functions & Polylogarithms >
Mathematica > Mathematics and Algorithms > Number Theory > Multiplicative Number Theory > Zeta Functions & Polylogarithms >
Built-in Mathematica SymbolTutorials »|See Also »|More About »

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)=sum_(k=1)^inftyk^(-s).
  • zeta(s,a)=sum_(k=0)^(infty)(k+a)^(-s), where any term with k+a=0 is excluded.
  • For Re(a)<0, the definition used is zeta(s,a)=sum_(k=0)^(infty)((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.
New in 1
Ask a question about this page  |  Suggest an improvement  |  Leave a message for the team