How to find the factorial of fractional numbers using matlab code?
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Athira T Das
le 16 Juil 2022
Commenté : Steven Lord
le 18 Juil 2022
I have an array s1. I want to evaluate the factorial of s1.
M=3;
m1 = 0:M;
s1 = m1./2
factorial(s1)
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John D'Errico
le 16 Juil 2022
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)
gamma(N + 1)
And the gamma function is defined on the real line. So...
gamma(1.5)
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)]
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.
2 commentaires
Rik
le 18 Juil 2022
It would be nice if Matlab would already suggest using the gamma function in the error message.
Steven Lord
le 18 Juil 2022
This sounds like a reasonable suggestion. I've added it to the enhancement database.
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