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Math Help - Proof of Decreasing Exponential Factorials properties

  1. #1
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    Proof of Decreasing Exponential Factorials properties

    I need help checking the following properties (whether they're true or false):

    x^{\underline{m.n}} = \prod_{k = 0}^{m-1} (x - kn)^\underline{n}

    x^{\underline{m.n}} = \prod_{k = 0}^{n-1} (x - km)^\underline{n}

    x^{\underline{m.n}} = \prod_{k = 0}^{n-1} (x - km)^\underline{m}

    where x^{\underline{m.n}} is a decreasing factorial exponential, i.e.:

     x^{\underline{m.n}} = \prod_{k = 0}^{m.n - 1} (x-k)

    Thanks in advance
    Last edited by greenday1209; May 1st 2011 at 06:46 AM. Reason: added further details
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by greenday1209 View Post
    I need help checking the following properties (whether they're true or false):

    x^{\underline{m.n}} = \prod_{k = 0}^{m-1} (x - kn)^\underline{n}

    x^{\underline{m.n}} = \prod_{k = 0}^{n-1} (x - km)^\underline{n}

    x^{\underline{m.n}} = \prod_{k = 0}^{n-1} (x - km)^\underline{m}

    where x^{\underline{m.n}} is a decreasing factorial exponential, i.e.:

     x^{\underline{m.n}} = \prod_{k = 0}^{m.n - 1} (x-k)

    Thanks in advance
    Numerical experiment shows that the second is false.

    If either the first or third is true then the other must also be true. Numerical experiment does not refute them.

    CB
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