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Article 11 — Appendix A.21n! — factorialCategory. Mathematics. Abstract. Factorial: definition, properties, identities and table of values for some arguments. References. This article is a part of scientific calculator LiL, scientific calculator LiX, scientific calculator LiLc and scientific calculator LiXc products. See also. Factorial generalization — gamma function Γ. 1. DefinitionFactorial is defined as 0! ≡ 1;n! ≡ 1×2×...×(n − 1) × n, for n = 1, 2, 3, ... From definition follows, that factorial is defined only for nonnegative integers, and its value is always positive integer. So, as function it is defined only at discrete points. 2. IdentitiesNext value identity (n + 1)! = (n + 1) n!There is a generalization of the factorial for real numbers — gamma function Γ — and n! = Γ(n + 1)3. CombinatoricsNumber of permutations — ordered ksize subsets of nelement set: ^{n}P_{k} = n! /(n − k)!Number of combinations — ksize subsets of nelement set: ^{n}C_{k} = n! / [k! (n − k)!]First dozen values
4. SupportFactorial 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 useTo calculate factorial of the number:
To calculate factorial of the current result:
To calculate factorial of the number n in memory:



