The Art of Mathematics

# fact — factorial

## 1. Definition

Factorial 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 non-negative integers, and its value is always positive integer. So, as function it is defined only at discrete points.

## 2. Combinatorics

Number of permutations — ordered k-size subsets of n-element set:

nPk = n! /(nk)!

Number of combinations — k-size subsets of n-element set:

nCk = n! / [k! (nk)!]

First dozen values

nn!
01
11
22
36
424
5120
6720
75040
840320
9362880
103628800
1139916800
12479001600
Table. 1. Factorial for some n.

## 4. How to use

To calculate factorial of the number:

``fact(8);``

To get factorial of the current result:

``fact(rslt);``

To get factorial of the number n in calculator memory:

``fact(mem[n]);``

## 5. Support

Factorial of the natural number and zero is supported in free version of the Librow calculator.

Factorial of the complex number — resolved into gamma function of the complex argument — is supported in professional version of the Librow calculator.