The word "factorial" is generally used on "whole integers", such as 2!, 14!, 25!.....etc.
If you have a number with a fraction such as 2.5!, 4.45!, 15.21!...., that is called the "Gamma function".
This Greek letter Γ, is called "capital gamma" and is used to calculate the Gamma function. So, for your question:Γ(.50) =0.886226^2 x 4 =π. You were curious about it, weren't you!!.
The word "factorial" is generally used on "whole integers", such as 2!, 14!, 25!.....etc.
If you have a number with a fraction such as 2.5!, 4.45!, 15.21!...., that is called the "Gamma function".
This Greek letter Γ, is called "capital gamma" and is used to calculate the Gamma function. So, for your question:Γ(.50) =0.886226^2 x 4 =π. You were curious about it, weren't you!!.
From its integral definition
\(\displaystyle \Gamma(x)=\int^{\infty}_{0}t^{x-1}e^{-t}\: dt\),
it can be shown that the gamma function has the property
\(\displaystyle \Gamma(x+1)=x\Gamma(x)\).
It can also be shown that \(\displaystyle \Gamma(1)=1\).
It follows that if x = n, where n = 0, 1, 2, ... , and where 0! = 1, that
\(\displaystyle \Gamma(n+1)=n!\)
This relationship holds only when n = 0, 1, 2, ... .
If n is negative or non-integer it becomes meaningless.
\(\displaystyle \Gamma(1.5) = \Gamma(0.5+1)=0.5\Gamma(0.5)\) for example, has a value, it is equal to \(\displaystyle \sqrt{\pi}/2 \approx 0.88623\) ,
but it's wrong to try to relate this to any particular factorial.
