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Math Help - factorials

  1. #1
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    factorials

    is n!*n! somehow related to (2n)!?

    thanks!

    To clarify:

    I'm trying to prove that (sorry for the bad formatting...)

    integral(cos(x*sin(theta)), theta, 0, pi/2) = c*J0(x)

    J0(x) is a bessel function of order zero.

    What I did:

    I turned the integral, or more specifically, the cos expression into the taylor series expression and also turned J0(x) into a series expression and am trying to cancel both sides. If n!*n! is equal to (2n)! or is somehow related by a constant or something it might be helpful.

    Otherwise, if you all can think of a more elegant way to prove it, I'm open to suggestions!
    Last edited by gsds; March 27th 2009 at 05:11 PM. Reason: to clarify
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  2. #2
    MHF Contributor

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    No, n!*n! is not equal to nor simply related to (2n)!. Just look at some values: if n= 2, 2!*2!= 4 while (2(2))!= 4!= 24. If n= 3, 3!*3!= 36 while (2(3))!= 6!= 720. You should be able to show that n!n! always divides (2n)! but there is no closer relationship than that.
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