Chapter 6.1, Problem 30P

(a)

To determine

To show: The $\Gamma \left(p+1\right)=p\Gamma \left(p\right)$ for $p>0$.

(b)

To determine

To show: The $\Gamma \left(1\right)=1$.

(c)

To determine

To show: The $\Gamma \left(n+1\right)=n!$ if p is a positive integer n.

(d)

To determine

To show: The $p\left(p+1\right)\left(p+2\right)\mathrm{...}\left(p+n-1\right)=\frac{\Gamma \left(p+n\right)}{\Gamma \left(p\right)}$ for $p>0$; find $\Gamma \left(\frac{3}{2}\right)$ and $\Gamma \left(\frac{11}{2}\right)$.