gives the hyperfactorial function .
- Mathematical function, suitable for both symbolic and numeric manipulation.
- 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.
Examplesopen allclose all
Basic 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:
Numerical Evaluation (4)
Specific Values (4)
For a simple parameter, Hyperfactorial gives exact values:
Plot the Hyperfactorial function:
Function Properties (11)
Real domain of Hyperfactorial:
Function range of Hyperfactorial on the contiguous portion of its domain:
Hyperfactorial threads elementwise over lists:
Hyperfactorial is not an analytic function:
Hyperfactorial is neither non-increasing nor non-decreasing:
Hyperfactorial is not injective:
Hyperfactorial is not surjective:
Hyperfactorial is neither non-negative nor non-positive:
Hyperfactorial has both singularities and discontinuities for x≤-1:
Hyperfactorial is neither convex nor concave:
The discriminant of the Hermite polynomial is related to the hyperfactorial:
Obtain Glaisher from a limit with Hyperfactorial and Exp functions:
Properties & Relations (2)
Hyperfactorial is produced in Product:
FindSequenceFunction can recognize the Hyperfactorial sequence:
Wolfram Research (2008), Hyperfactorial, Wolfram Language function, https://reference.wolfram.com/language/ref/Hyperfactorial.html.
Wolfram Language. 2008. "Hyperfactorial." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Hyperfactorial.html.
Wolfram Language. (2008). Hyperfactorial. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Hyperfactorial.html