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 is identical to Zeta for .
- Unlike Zeta, HurwitzZeta has singularities at for non-negative integers .
- 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.
- HurwitzZeta automatically threads over lists.
Examplesopen allclose all
Basic Examples (6)
Series expansion at Infinity:
Numerical Evaluation (4)
Specific Values (5)
Function Properties (4)
Compute the indefinite integral using Integrate:
Series Expansions (2)
Find the Taylor expansion using Series:
Function Identities and Simplifications (2)
HurwitzZeta is defined through the identity:
Properties & Relations (2)
Introduced in 2008