Chapter 11.5, Problem 3P

In Chapter 1, $equations(13.5)and$

(13.6), we defined the binomial coefficients $\left(\begin{array}{l}p\hfill \\ n\hfill \end{array}\right)$ where $n$ is a non-negative integer but $p$ may be negative or fractional. Show that (p) can be written in terms of $\Gamma$ functions as $\left(\begin{array}{l}p\hfill \\ n\hfill \end{array}\right)=\frac{\Gamma (p+1)}{n!\Gamma (p-n+1)}$.