How to find the factorial of fractional numbers using matlab code?

I have an array s1. I want to evaluate the factorial of s1.

M=3;
m1 = 0:M;
s1 = m1./2

s1 = 1×4

0 0.5000 1.0000 1.5000

factorial(s1)

Error using factorial
N must be an array of real non-negative integers.

Answer 1

[John D'Errico]

You CANNOT compute the factorial of a fractional number. Factorials are defined only for integers.

HOWEVER...

It is true that

factorial(N) == gammma(N+1)

for integer N. You might think of the gamma function as an extension of the factorial function onto the real line. For example:

N = 0:10;
factorial(N)

ans = 1×11

1 1 2 6 24 120 720 5040 40320 362880 3628800

gamma(N + 1)

ans = 1×11

1 1 2 6 24 120 720 5040 40320 362880 3628800

And the gamma function is defined on the real line. So...

gamma(1.5)

ans = 0.8862

is thus what you might think of when you write (0.5)!.

fplot(@gamma,[.1,5])

In fact, the gamma function follows the smiple rules that work for factorial. Thus we would see that if

factorial(N) == N*factorial(N-1)

then we might hope it would be true that

gamma(N+1) = N*gamma(N)

For example, we can test that as:

format long g
[gamma(3.25)*3.25,gamma(4.25)]

ans = 1×2

8.28508514183522 8.28508514183522

So the gamma function follows a similar recursive rule like the factorial function. The only differnce is you don't have any easy way to start the recursion.

[Rik]

It would be nice if Matlab would already suggest using the gamma function in the error message.

[Steven Lord]

This sounds like a reasonable suggestion. I've added it to the enhancement database.