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# factorial

Factorial function

factorial(n)
factorial(A)

## Description

factorial(n) returns the factorial of n.

factorial(A) returns the factorials of each element of A.

## Input Arguments

 n Symbolic variable or expression representing a nonnegative integer. A Vector or matrix of symbolic variables or expressions representing nonnegative integers.

## Examples

Compute the factorial function for these expressions:

```syms n
f = factorial(n^2 + 1)```
```f =
factorial(n^2 + 1)```

Now substitute the variable n with the value 3:

`subs(f, n, 3)`
```ans =
3628800```

Differentiate the expression involving the factorial function:

```syms n
diff(factorial(n^2 + n + 1))```
```ans =
factorial(n^2 + n + 1)*psi(n^2 + n + 2)*(2*n + 1)```

Expand the expression involving the factorial function:

```syms n
expand(factorial(n^2 + n + 1))```
```ans =
factorial(n^2 + n)*(n^2 + n + 1)```

Compute the limit for the expression involving the factorial function:

```syms n
limit(factorial(n)/exp(n), n, inf)```
```ans =
Inf```

Call factorial for the matrix A. The result is a matrix of the factorial functions:

```A = sym([1 2; 3 4]);
factorial(A)```
```ans =
[ 1,  2]
[ 6, 24]```

expand all

### Factorial Function

This product defines the factorial function of a positive integer:

$n!=\prod _{k=1}^{n}k$

The factorial function 0! = 1.

### Tips

• Calling factorial for a number that is not a symbolic object invokes the MATLAB® factorial function.