Hyperfactorial
gives the hyperfactorial function .
Details

- Mathematical function, suitable for both symbolic and numeric manipulation.
- Hyperfactorial is defined as
for positive integers
.
- Hyperfactorial is defined as
for positive integers
and is otherwise defined as
.
- The hyperfactorial function satisfies
.
- Hyperfactorial can be evaluated to arbitrary numerical precision.
- Hyperfactorial automatically threads over lists.
Examples
open allclose allBasic Examples (5)
Plot over a subset of the reals:
Plot over a subset of the complexes:
Series expansion at the origin:
Series expansion at Infinity:
Scope (19)
Numerical Evaluation (4)
Specific Values (4)
For a simple parameter, Hyperfactorial gives exact values:
Visualization (2)
Function Properties (4)
Real domain of Hyperfactorial:
Function range of Hyperfactorial:
Hyperfactorial threads elementwise over lists:
TraditionalForm formatting:
Differentiation (2)
Properties & Relations (2)
Hyperfactorial is produced in Product:
FindSequenceFunction can recognize the Hyperfactorial sequence:
Text
Wolfram Research (2008), Hyperfactorial, Wolfram Language function, https://reference.wolfram.com/language/ref/Hyperfactorial.html.
BibTeX
BibLaTeX
CMS
Wolfram Language. 2008. "Hyperfactorial." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Hyperfactorial.html.
APA
Wolfram Language. (2008). Hyperfactorial. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Hyperfactorial.html