Thread: binomial coefficient

(1+x)^-0.5 - Wolfram|Alpha

I don't understand the coefficient of the general term given when mod. x <1. I have only seen positive integers before.

Originally Posted by Stuck Man

I don't understand the coefficient of the general term given when mod. x <1. I have only seen positive integers before.

If $\displaystyle p\in\mathbb{R},\;n\in \mathbb{N}$ we define $\displaystyle \displaystyle\binom{p}{n}=\dfrac{p(p-1)\ldots (p-n+1)}{n!}.$ For example $\displaystyle \displaystyle\binom{-0.5}{3}=\dfrac{(-0.5)(-0.5-1)(-0.5-2)}{3!}=\ldots$

Thanks. I thought that way of evaluating nCr was simply convenient sometimes.