For alternative uses of the exclamation point symbol, please see double factorial for expressions of the form 4!! or subfactorial for expressions of the form !3 .
- $ n!\equiv1\cdot2\cdot3\cdots n $
The notation $ n! $ is read "$ n $ factorial". Alternatively, one could think of the product as being in the opposite order:
- $ n!\equiv n(n-1)(n-2)\cdots3\cdot2\cdot1 $
As a consequence of the empty product,
- $ 0!\equiv1 $
As a concrete example:
- $ 5!=1\cdot2\cdot3\cdot4\cdot5=120 $
The factorial function can also be seen as a specific case of the gamma function ($ \Gamma $), which extends the factorial to the complex plane (excluding the non-positive integers). In particular, for all values for which the factorial is defined:
- $ n!=\Gamma(n+1) $
- Fast Factorial Functions: Contains algorithms for computing large factorials.