(a) I want to find a formula for the above and then prove it by induction. The answer according to Wolfram is $n!$, however I have no idea how to get there. Any hints or ideas on how I should tackle this one?
(b) Also, I want to understand why it is called is Gamma Function!
(c) Finally, it is difficult to understand what is factorial of non natural number? (For example Wolfram tells me that $3.5! = 11.6317$.)