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HurwitzZeta

HurwitzZeta[s, a]
gives the Hurwitz zeta function zeta(s,a).
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • The Hurwitz zeta function is defined as an analytic continuation of zeta(s,a)=sum_(k=0)^(infty)(k+a)^(-s).
  • HurwitzZeta has branch cut discontinuities in the complex a plane running from 0 to -infty.
  • For certain special arguments, HurwitzZeta automatically evaluates to exact values.
  • HurwitzZeta can be evaluated to arbitrary numerical precision.
EXAMPLESCLOSE ALL
Scope   (6)
Evaluate numerically:
Evaluate for complex arguments:
Evaluate to arbitrary precision:
The precision of the output tracks the precision of the input:
Evaluate exactly:
HurwitzZeta threads element-wise over lists:
TraditionalForm formatting:
Properties & Relations   (2)
HurwitzZeta can be generated by symbolic solvers:
For Re(a)>0 two-argument Zeta coincides with HurwitzZeta:
Possible Issues   (2)
HurwitzZeta differs from the two-argument form of Zeta by a different choice of branch cut:
HurwitzZeta includes singular terms, unlike Zeta:
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