Can anyone tell me if there are any implications of squaring a gamma function as shown below?
$$\left(\frac{L\Gamma(8)\Gamma(\frac{11}{2})}{\Gamma(\frac{9}{2})\Gamma(9)}\right)^2$$
I just want to know if it's alright to distribute the exponent to the rest of the expression such that it'll be
$$\frac{L^2\Gamma^2(8)\Gamma^2(\frac{11}{2})}{\Gamma^2(\frac{9}{2})\Gamma^2(9)}$$
For context, L is just a constant and the following expression above is what I have acquired after solving for the first moment of a probability density function.
Essentially, $\Gamma ( n)$ is just a constant for almost all constant, rational n.
So you are allowed to treat it in the same way as you would treat any other constant.