Zeta

Zeta[s]

gives the Riemann zeta function .

Zeta[s,a]

gives the generalized Riemann zeta function .

Details 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.

Examples

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Basic Examples  (3)

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Generalized (Hurwitz) zeta function:

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Scope  (14)

Applications  (7)

Properties & Relations  (8)

Possible Issues  (4)

Neat Examples  (2)

See Also

PolyLog  HarmonicNumber  LerchPhi  HurwitzZeta  RiemannSiegelZ  ZetaZero  StieltjesGamma  Glaisher  PrimePi  DirichletL  RamanujanTauL  PrimeZetaP  DirichletTransform

Tutorials

Introduced in 1988
(1.0)