>>14359863The gamma function is how they represent a factorial as a continuous function. The problem is....how do you actually calculate values from the gamma function? I don't know if it has a series representation. If you read the wikipedia page, they have various programmatical tricks for getting these values, but they're far from straightforward.
So that means that if you plan to solve the function in OP, you're going to need to express the answer in terms of the gamma function, or related functions
https://mathworld.wolfram.com/GammaFunction.html 
