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Math Help - Gamma Function logarithmic derivative

  1. #1
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    Gamma Function logarithmic derivative

    Show that -\frac{\Gamma'}{\Gamma}(z)=\gamma + \frac{1}{z} + \sum_{j=1}^\infty(\frac{1}{z+j}-\frac{1}{j})

    Hint: use Weierstrass product formula \frac{1}{\Gamma (s)}=se^{\gamma s} \prod_{n=1}^{\infty}(1 + \frac{s}{n})e^{-s/n}
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  2. #2
    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by EinStone View Post
    Show that -\frac{\Gamma'}{\Gamma}(z)=\gamma + \frac{1}{z} + \sum_{j=1}^\infty(\frac{1}{z+j}-\frac{1}{j})

    Hint: use Weierstrass product formula \frac{1}{\Gamma (s)}=se^{\gamma s} \prod_{n=1}^{\infty}(1 + \frac{s}{n})e^{-s/n}
    Double post... tisk tisk tisk
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  3. #3
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    I first thought posting didnt work in the other thread so I decided to change forum, but now its double and I didnt see how to delete, sry.
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  4. #4
    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by EinStone View Post
    I first thought posting didnt work in the other thread so I decided to change forum, but now its double and I didnt see how to delete, sry.
    Haha, it's ok
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