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 Documentation / Mathematica / Built-in Functions / Mathematical Functions / Zeta Related  /
Zeta

  • Zeta[ s ] gives the Riemann zeta function .
  • Zeta[ s , a ] gives the generalized Riemann zeta function .
  • Mathematical function (see Section A.3.10).
  • .
  • , where any term with is excluded.
  • Zeta[ s ] has no branch cut discontinuities.
  • See the Mathematica book: Section 3.2.10.
  • See also: PolyLog, LerchPhi, RiemannSiegelZ, StieltjesGamma, PrimePi.
  • Related package: NumberTheory`Ramanujan`.

    Further Examples

    If the real part of s is greater than , this sum is Zeta[s].

    In[1]:=

    Out[1]=

    Exact values can be calculated at the positive even integers.

    In[2]:=

    Out[2]=