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Math Help - binomial coefficient

  1. #1
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    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.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: binomial coefficient

    Quote Originally Posted by Stuck Man View Post
    I don't understand the coefficient of the general term given when mod. x <1. I have only seen positive integers before.
    If p\in\mathbb{R},\;n\in \mathbb{N} we define \displaystyle\binom{p}{n}=\dfrac{p(p-1)\ldots (p-n+1)}{n!}. For example \displaystyle\binom{-0.5}{3}=\dfrac{(-0.5)(-0.5-1)(-0.5-2)}{3!}=\ldots
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  3. #3
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    Re: binomial coefficient

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