Factorial

The product of the positive integers up to n, written n!.

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Factorial(n), the product of the integers from 1 to n.

SageMathfactorial(n)SymPyfactorial(n)

Domain: Combinatorics

Details

by convention, the empty product.
Recurrence: .
Extends to non-integers via the Gamma function, , so half-integer factorials involve .
Grows faster than any exponential; Stirling's approximation describes the asymptotics.
compute-engine returns ComplexInfinity at negative integers, the poles of Gamma, rather than leaving the expression unevaluated.

Examples

See also: Binomial, Factorial2, Subfactorial, Pochhammer