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Math Help - How to write "n choose k" as x^n y^k z^(n-k) without using Stirling

  1. #1
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    How to write "n choose k" as x^n y^k z^(n-k) without using Stirling

    Hi,

    Is there a way to write the combinatorial (n choose k) as:

    {n \choose k} =Const. \cdot x^n y^k z^{n-k}

    Without using Stirling's formula and without having a product or summation in x, y and z?

    What could x=x(n,k), y=y(n,k) and z=z(n,k) be?

    Thanks,

    Gerrit
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  2. #2
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    Re: How to write "n choose k" as x^n y^k z^(n-k) without using Stirling

    Hey gerritgroot.

    You may be able to use an integral representation, but the integral itself won't have a nice analytic answer if you try and evaluate it. If you are still interested, you probably want to check out the Beta Integral:

    Beta function - Wikipedia, the free encyclopedia
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  3. #3
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    Re: How to write "n choose k" as x^n y^k z^(n-k) without using Stirling

    Thanks, I will check that
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