Chapter 8.8, Problem 99E

The Gamma Function The Gamma Function $\Gamma (n)$ isdefined by $\Gamma (n)={\displaystyle {\int }_0^{\infty }{x}^{n-1}{e}^{-x}dxn>0}$

(a) Find $\Gamma (1),\Gamma (2)$

), and $\Gamma (3)$.

(b) Use integration by parts to show that $\Gamma (n+1)=n\Gamma (n)$.

(c) Write I'(n) using factorial notation where n is a positiveinteger.