Mathematica > Mathematics and Algorithms > Mathematical Functions > Special Functions > Zeta Functions & Polylogarithms > Zeta
Mathematica > Mathematics and Algorithms > Number Theory > Analytic Number Theory > Zeta Functions & Polylogarithms > Zeta
Mathematica > Mathematics and Algorithms > Number Theory > Multiplicative Number Theory > Zeta Functions & Polylogarithms > Zeta
BUILT-IN MATHEMATICA SYMBOL

Zeta

Zeta[s]
gives the Riemann zeta function .

Zeta[s, a]
gives the generalized Riemann zeta function .

Details and OptionsDetails and Options

  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • For Re(s)>1, .
  • , where any term with is excluded.
  • For Re(a)<0, the definition used is .
  • 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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