Need help with finding if a function has a name.

Question

I watched a first year senior year class in China and saw a function on the board.

$$ H^n_x = x(x+1)(x+2)\cdots (x+n-1)$$

you can see a similar problem here in Chinese.

I think this function has name, but I haven't found it. I have searched Stirling Formula, Gamma Function, etc but haven't found this particular function.

My question is does $H^n_x$ have a specific name and help me find some resources to read more about this function.

Answer 1

Rising factorial though Wikipedia also calls it the "Pochhammer function", "Pochhammer polynomial", "ascending factorial", "rising sequential product" or "upper factorial"