factorial

Factorial of symbolic input

Syntax

f = factorial(n)

Description

f = factorial(n) returns the factorial of n. If n is an array, factorial acts element-wise on n.

Examples

Factorial for Symbolic Number

Compute the factorial for a symbolic number.

f = factorial(sym(20))

f = $$2432902008176640000$$

Compute Factorial Function for Symbolic Expression

Compute the factorial function for a symbolic expression. factorial returns exact symbolic output as the function call.

syms n
expr = n^2 + 1;
f = factorial(expr)

f = $$\left(n^2+1\right)!$$

Calculate the factorial for a value of n = 3. Substitute the value of n by using subs.

fVal = subs(f,n,3)

fVal = $$3628800$$

Differentiate Factorial Function

Differentiate an expression containing the factorial function $\left({\mathit{n}}^2+\mathit{n}+1\right)!$

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

f = $$\left(n^2+n+1\right)!$$

df = diff(f)

df = $$\left(n^2+n+1\right)!\hspace{0.17em}\psi \text{<a href="matlab:doc symbolic/psi">psi</a>}\left(n^2+n+2\right)\hspace{0.17em}\left(2\hspace{0.17em}n+1\right)$$

The derivative of the factorial function is expressed in terms of the psi function.

Expand Factorial Function

Expand an expression containing the factorial function.

syms n
f = factorial(n^2 + n + 1);
f1 = expand(f)

f1 = $$\left(n^2+n\right)!\hspace{0.17em}\left(n^2+n+1\right)$$

Limit of Factorial Function

Compute the limit at infinity for an expression containing the factorial function.

syms n
f = factorial(n)/exp(n);
fLim = limit(f,n,Inf)

fLim = $$\infty$$

Compute Factorial for Array Input

Compute factorial for array input. factorial acts element-wise on array input.

A = sym([1 3; 4 5]);
f = factorial(A)

f = 
$$\left(\begin{array}{cc}1& 6\\ 24& 120\end{array}\right)$$

Input Arguments

n — Input

number | vector | matrix | array | symbolic number | symbolic variable | symbolic array | symbolic function | symbolic expression

Input, specified as a number, vector, matrix, or array, or a symbolic number, variable, array, function, or expression.

More About

Factorial Function

The factorial of a number n is defined as follows.

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

The factorial of 0 is 1.

Tips

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

Version History

Introduced in R2012a