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## Examples of use of n!

### Combinatorics

The binomial coefficient of the natural number n and the integer k is defined to be the natural number:

and

### Partial derivative

### Stirling's formula

Asymptotic series expansions

### Function with n!

Gamma function.

If the real part of the complex number z is positive, then the following integral converges absolutely:
.

In particular, using integration by parts, we can show that:
.

Stirling's approximation:

http://mathworld.wolfram.com/StirlingsApproximation.html

Factorial and permutations:

http://mathworld.wolfram.com/Factorial.html

96 other formulas with this notation:

http://functions.wolfram.com/GammaBetaErf/Factorial/

Gamma and Beta functions:

http://functions.wolfram.com/GammaBetaErf/

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