AlternatingFactorial
gives the alternating factorial .
Details

- Mathematical function, suitable for both symbolic and numerical manipulation.
- The
satisfies the recurrence relation
with
.
- AlternatingFactorial can be evaluated to arbitrary numerical precision.
- AlternatingFactorial automatically threads over lists.
- AlternatingFactorial can be used with Interval and CenteredInterval objects. »
Examples
open allclose allBasic Examples (6)
Compute the first several alternating factorial numbers:
Plot the values on a log scale over a subset of the reals:
Plot over a subset of the complexes:
Expand the alternating factorial in terms of other functions:
Give the closed form of the following alternating sum:
The alternating factorial numbers give the solution to the following recurrence:
Scope (17)
Numerical Evaluation (4)
Evaluate efficiently at high precision:
AlternatingFactorial can be used with Interval and CenteredInterval objects:
Specific Values (3)
Visualization (2)
Plot the absolute value of AlternatingFactorial:
Function Properties (8)
Real domain of AlternatingFactorial:
AlternatingFactorial threads elementwise over lists:
AlternatingFactorial is not an analytic function:
AlternatingFactorial has both singularity and discontinuity for z≤-2:
AlternatingFactorial is neither nondecreasing nor nonincreasing:
AlternatingFactorial is not injective:
AlternatingFactorial is neither non-negative nor non-positive:
It is non-negative on the non-negative reals:
AlternatingFactorial is neither convex nor concave:
Applications (1)
As a definition, the following sum is AlternatingFactorial:
Text
Wolfram Research (2014), AlternatingFactorial, Wolfram Language function, https://reference.wolfram.com/language/ref/AlternatingFactorial.html.
CMS
Wolfram Language. 2014. "AlternatingFactorial." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/AlternatingFactorial.html.
APA
Wolfram Language. (2014). AlternatingFactorial. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/AlternatingFactorial.html