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Content |
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Algorithms |
A very short description of 21 algorithms for computing the factorial function n!. |
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Julia factorial |
*NEW* The factorial function based on the swinging factorial which in turn is computed
via prime factorization implemented in Julia. |
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Mini Library |
The factorial function, the binomial function, the
double factorial, the swing numbers and an efficient
prime number sieve implemented in Scala and GO. |
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Browse Code |
Various algorithms implemented in
Java, C# and C++. |
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SageMath |
Implementations in SageMath. |
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LISP |
Implementations in Lisp. |
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Benchmarks |
Benchmark 2013:
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. |
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Conclusions |
Which algorithm should we choose? |
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Download |
Download a test application and benchmark yourself. |
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Approximations |
A unique collection! Approximation formulas. |
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Gamma quot |
Bounds for Gamma(x+1)/Gamma(x+1/2) |
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Gamma shift |
Why is Gamma(n)=(n-1)! and not Gamma(n)=n! ? |
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Hadamard
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Hadamard's Gamma function and a new factorial function
[MathJax version] |
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History |
Not even Wikipedia knows this!
The early history of the factorial function. |
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Notation |
On the notation n! |
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Binary Split |
For coders only. Go to the page of the day. |
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Sage / Python |
Implementation of the swing algorithm. |
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Double Factorial |
The fast double factorial function. |
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Prime Factorial |
Primfakultaet ('The Primorial', in German.) |
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Bibliography |
Bibliography on Inequalities for the Gamma function. |
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Bernoulli &
Euler |
Exotic Applications:
Inclusions for the Bernoulli and Euler numbers. |
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Binomial |
Fast Binomial Function (Binomial Coefficients). |
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Variations |
A combinatorial generalization of the factorial. |
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Stieltjes'
CF |
On Stieltjes' Continued Fraction for the
Gamma Function. |
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al-Haytham /
Lagrange |
The ignorance of some western mathematicians.
A deterministic factorial primality test. |
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Factorial Digits |
Number of decimal digits of 10n! |
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Calculator |
Calculate n! for n up to 9.999.999.999 . |
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RPN-Factorial |
The retro-factorial page! |
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Permutations |
Awesome! Permutation trees, the combinatorics of n!.
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Perm. trees |
Download a pdf-poster
with 120 permutation trees! |
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Gamma
LogGamma |
Plots of the factorial (gamma) function. |
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External links |
Some bookmarks. |