Details and Options
- Mathematical function, suitable for both symbolic and numerical manipulation.
- For , .
- , where any term with is excluded.
- For , 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.
- Zeta can be used with Interval and CenteredInterval objects. »
Examplesopen allclose all
Basic Examples (6)
Series expansion at Infinity:
Numerical Evaluation (6)
Specific Values (6)
Function Properties (12)
Real domain of Zeta:
Zeta achieves all real values:
Zeta has the mirror property :
Zeta threads elementwise over lists and matrices:
Zeta is not an analytic function:
Zeta is neither non-decreasing nor non-increasing:
Zeta is not injective:
Zeta is surjective:
Zeta is neither non-negative nor non-positive:
Series Expansions (2)
Use MellinTransform to find the first two terms in the asymptotic expansion for a function that is defined by an infinite series:
Compute the residues at and to obtain the required asymptotic expansion represented with Zeta function:
Properties & Relations (8)
Riemann Zeta Function (5)
Generalized Zeta Function (3)
In certain cases, FunctionExpand gives formulas in terms of other functions:
Possible Issues (4)
In TraditionalForm, ζ is not automatically interpreted as the zeta function:
Wolfram Research (1988), Zeta, Wolfram Language function, https://reference.wolfram.com/language/ref/Zeta.html (updated 2022).
Wolfram Language. 1988. "Zeta." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2022. https://reference.wolfram.com/language/ref/Zeta.html.
Wolfram Language. (1988). Zeta. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Zeta.html