gives the alternating factorial .


  • 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.


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Basic 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  (11)

Numerical Evaluation  (3)

Evaluate numerically:

Evaluate to high precision:

Evaluate efficiently at high precision:

Specific Values  (3)

Values of AlternatingFactorial at fixed points:

Value at zero:

Evaluate symbolically:

Visualization  (2)

Plot the absolute value of AlternatingFactorial:

Plot the real part of :

Plot the imaginary part of :

Function Properties  (3)

Real domain of AlternatingFactorial:

Complex domain:

AlternatingFactorial threads elementwise over lists:

Show a typeset form:

Wolfram Research (2014), AlternatingFactorial, Wolfram Language function,


Wolfram Research (2014), AlternatingFactorial, Wolfram Language function,


@misc{reference.wolfram_2021_alternatingfactorial, author="Wolfram Research", title="{AlternatingFactorial}", year="2014", howpublished="\url{}", note=[Accessed: 26-October-2021 ]}


@online{reference.wolfram_2021_alternatingfactorial, organization={Wolfram Research}, title={AlternatingFactorial}, year={2014}, url={}, note=[Accessed: 26-October-2021 ]}


Wolfram Language. 2014. "AlternatingFactorial." Wolfram Language & System Documentation Center. Wolfram Research.


Wolfram Language. (2014). AlternatingFactorial. Wolfram Language & System Documentation Center. Retrieved from