Currently there may be errors shown on top of a page, because of a missing Wiki update (PHP version and extension DPL3).
Navigation
Topics Help • Register • News • History • How to • Sequences statistics • Template prototypes

Difference between revisions of "Factorial number"

From Prime-Wiki
Jump to: navigation, search
m (Karbon moved page Factorial to Factorial number without leaving a redirect: name)
(see also Factorial prime)
 
(One intermediate revision by the same user not shown)
Line 4: Line 4:
 
A factorial is defined by the product
 
A factorial is defined by the product
 
:<math>n!  = 1 \cdot 2 \cdot 3 \cdots (n{-}2) \cdot (n{-}1) \cdot n</math>
 
:<math>n!  = 1 \cdot 2 \cdot 3 \cdots (n{-}2) \cdot (n{-}1) \cdot n</math>
for <math>n &ge; 1</math>.
+
for <math>n \ge 1</math>.
  
 
The same written as mathmatical product
 
The same written as mathmatical product
Line 17: Line 17:
  
 
==See also==
 
==See also==
 +
*[[Factorial prime]]
 
*[[Multifactorial number]]
 
*[[Multifactorial number]]
  

Latest revision as of 13:40, 5 November 2023

In mathematics symbolized by placing the "!" (known as the exclamation mark or bang) after a number, it represents multiplying a number by all whole numbers smaller than it.

Definition

A factorial is defined by the product

[math]\displaystyle{ n! = 1 \cdot 2 \cdot 3 \cdots (n{-}2) \cdot (n{-}1) \cdot n }[/math]

for [math]\displaystyle{ n \ge 1 }[/math].

The same written as mathmatical product

[math]\displaystyle{ n! = \prod_{i = 1}^n i. }[/math]

and as recurrence relation

[math]\displaystyle{ n! = n \cdot (n-1)! }[/math]

Examples

5! = 5 * 4 * 3 * 2 * 1 = 120
10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 3628800

See also

External links