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Math Help - Show that this is a constant

  1. #1
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    Show that this is a constant

    I want to prove Legendre's doublign formula, and I want to show the following in order to do that. (Note that I don't want a proof of the doubling formula)

    log\Gamma(s)-log\Gamma(\frac{s}{2})-log\Gamma(\frac{s+1}{2})-s* log 2 is a constant.
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  2. #2
    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by EinStone View Post
    I want to prove Legendre's doublign formula, and I want to show the following in order to do that. (Note that I don't want a proof of the doubling formula)

    log\Gamma(s)-log\Gamma(\frac{s}{2})-log\Gamma(\frac{s+1}{2})-s* log 2 is a constant.
    I would raise take that formula and raise it to the power  e , then use this definition of  \Gamma(s) :

     \Gamma(s) = \lim_{n\to\infty} \frac{n^s(n-1)!}{s(s+1)\cdots(s+n-1)} .
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  3. #3
    MHF Contributor chiph588@'s Avatar
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    Also, I would let  s \mapsto 2s . It makes cancellation easier.
    Last edited by chiph588@; April 8th 2010 at 06:43 PM.
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