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HurwitzZeta

HurwitzZeta
gives the Hurwitz zeta function .
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • The Hurwitz zeta function is defined as an analytic continuation of .
  • HurwitzZeta has branch cut discontinuities in the complex plane running from to .
  • For certain special arguments, HurwitzZeta automatically evaluates to exact values.
  • HurwitzZeta can be evaluated to arbitrary numerical precision.
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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:
HurwitzZeta can be generated by symbolic solvers:
For two-argument Zeta coincides with HurwitzZeta:
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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