Factorial

The factorial n ! 𝑛 n! of a Natural Number n 𝑛 n is the product of all positive integers less than or equal to n 𝑛 n .

n!=1×2×⋯×(n−2)×(n−1)×n=∏k=1n=k𝑛12⋯𝑛2𝑛1𝑛superscriptsubscriptproduct𝑘1𝑛𝑘n!=1\times 2\times\cdots\times(n-2)\times(n-1)\times n=\prod_{k=1}^{n}=k

Equivalently, n ! 𝑛 n! can be described by the following Recurrance Relation:

0!0\displaystyle 0! =1absent1\displaystyle=1
(n+1)!𝑛1\displaystyle(n+1)! =(n+1)⁢n!absent𝑛1𝑛\displaystyle=(n+1)n!

Asymptotics

Factorials grow faster than Exponential Functions, but slower than Double Exponential Functions.