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

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I have an array s1. I want to evaluate the factorial of s1.
m1 = 0:M;
s1 = m1./2
s1 = 1×4
0 0.5000 1.0000 1.5000
Error using factorial
N must be an array of real non-negative integers.

Accepted Answer

John D'Errico
John D'Errico on 16 Jul 2022
You CANNOT compute the factorial of a fractional number. Factorials are defined only for integers.
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;
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...
ans = 0.8862
is thus what you might think of when you write (0.5)!.
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
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.
Steven Lord
Steven Lord on 18 Jul 2022
This sounds like a reasonable suggestion. I've added it to the enhancement database.

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