/vt/ - Virtual Youtubers

Petra was asking yesterday how to integrate a factorial.

Well you see the factorial is only well defined for discrete values.
1!, 2!, 3!.....etc. It has to be an integer
But mathematicians have turned the factorial into a continuous function, using something called the Gamma Function:
>https://en.wikipedia.org/wiki/Gamma_function

The problem with this, is that calculating the gamma function is not trivial at ALL. It usually involves some really tricky programmatical tricks to approximate the answer. It's not like a convenient thing. To integrate the gamma function is not an easy task either. You can use a program to approximate this integral though. But it's not some easy calculation, you need to write a script that will go in and do this.

When it comes to things like the Gamma Function and the Riemann Zeta Function, integrating them isn't really of primary interest anyway. In fact what might be of greater interest is finding the contour integral, or residue of these functions. And as you can see:
>https://www.hindawi.com/journals/jmath/2013/181724/
It's super easy.