In Chapter 1, equations (13.5) and (13.6), we defined the binomial coefficients$$\begin{gathered} \left(p \\ n\right) \end{gathered}$$whereis a non-negative integer butmay be negative or fractional. Show that$$\begin{gathered} \left(p \\ n\right) \end{gathered}$$ can be written in terms of$\mathit{\Gamma }$functions as

role="math" localid="1664340642097" $\left(\frac{p}{n}\right)\mathbf{=}\frac{{\displaystyle \Gamma \left(p+1\right)}}{\mathbf{n}\mathbf{!}{\displaystyle \Gamma }{\displaystyle (}{\displaystyle p}{\displaystyle -}{\displaystyle n}{\displaystyle +}{\displaystyle 1}{\displaystyle )}}$

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!