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Article 11 — Appendix A.21
Abstract. Factorial: definition, properties, identities and table of values for some arguments.
See also. Factorial generalization — gamma function Γ.
Factorial is defined as0! ≡ 1;
n! ≡ 1×2×...×(n − 1) × n, for n = 1, 2, 3, ...
From definition follows, that factorial is defined only for non-negative integers, and its value is always positive integer. So, as function it is defined only at discrete points.
Next value identity(n + 1)! = (n + 1) n!
There is a generalization of the factorial for real numbers — gamma function Γ — andn! = Γ(n + 1)
Number of permutations — ordered k-size subsets of n-element set:nPk = n! /(n − k)!
Number of combinations — k-size subsets of n-element set:nCk = n! / [k! (n − k)!]
First dozen values
Factorial n! is supported in:
Factorial of the real number n!=x! (resolved into gamma function) is supported in:
Factorial of the complex number n!=z! (resolved into gamma function of the complex argument) is supported in:
5. How to use
To calculate factorial of the number:
To calculate factorial of the current result:
To calculate factorial of the number n in memory: