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Definition

For $k \in \mathbb{N}$ a natural number, its factorial $k! \in \mathbb{N}$ is the number obtained by multiplying all positive natural numbers less than or equal to $k$:

In combinatorics, the definition usually extends to $k = 0$ by setting $0! = 1$. This may be justified by defining $k!$ to be the number of permutations of a set with $k$ elements.

Related concepts

• double factorial

• binomial coefficient, multinomial coefficient

• Gamma function

• Euler beta function

• exponential series

References

See also

• Wikipedia, Factorial