
Link  Content  
Algorithms  A very short description of 21 algorithms for computing the factorial function n!. 

X  FFFMiniLib 
The factorial function, the binomial function, the double factorial, the swing numbers and an efficient prime number sieve implemented in Scala and GO. 
Browse Code  Various algorithms implemented in Java, C# and C++.  
Benchmarks  New. Benchmark 2013 is out! With MPIR 2.6 you can calculate 100.000.000! in less than a minute provided you use one of the fast algorithms described here.  
Conclusions  Which algorithm should we choose?  
Download  Download a test application and benchmark yourself.  
X  Approximations  A unique collection! Approximation formulas. 
Gamma quot  Bounds for Gamma(x+1)/Gamma(x+1/2)  
Gamma shift  Why is Gamma(n)=(n1)! and not Gamma(n)=n! ?  
X 
Hadamard 
Hadamard's Gamma function and a new factorial function [MathJax version] 
History  Not even Wikipedia knows this! The early history of the factorial function. 

Notation  On the notation n!  
Binary Split  For coders only. Go to the page of the day.  
Sage / Python  Implementation of the swing algorithm.  
‼  Double Factorial  The fast double factorial function. 
Prime Factorial  Primfakultaet ('The Primorial', in German.)  
Bibliography  Bibliography on Inequalities for the Gamma function.  
X  Bernoulli & Euler 
Exotic Applications: Inclusions for the Bernoulli and Euler numbers. 
Binomial  Fast Binomial Function (Binomial Coefficients).  
Variations  A combinatorial generalization of the factorial.  
X  Stieltjes' CF  On Stieltjes' Continued Fraction for the Gamma Function. 
alHaytham / Lagrange 
The ignorance of some western mathematicians. A deterministic factorial primality test. 

Factorial Digits  Number of decimal digits of 10^{n}!  
Calculator  Calculate n! for n up to 9.999.999.999 .  
RPNFactorial  The retrofactorial page!  
Permutations  Awesome! Permutation trees, the combinatorics of n!.  
Perm. trees  Download a pdfposter with 120 permutation trees!  
Gamma LogGamma 
Plots of the factorial (gamma) function.  
External links  Some bookmarks. 
Visit also our survey of the Bernoulli numbers on the occasion of the 300th
anniversary of the publication of
Jacob Bernoulli's Ars Conjectandi, 17132013.