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Integral representation of the Euler-Mascheroni constant

  1. Jun 9, 2012 #1
    I am trying to prove a specific representation of Euler's constant, but I am not really getting anywhere. I hoped you could help me with this one, because I looked it up on the Internet and even though the relation itself is found in many webpages, its proof is in none. The relation is
    [tex]\gamma=-\int_{0}^{\infty}e^{-t}\log(t)dt[/tex]
    I tried integrating by parts and integrating term by term using power series, but none of them show the identity. Thanks for your help from now.
     
  2. jcsd
  3. Jun 9, 2012 #2

    micromass

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  4. Jun 9, 2012 #3
    Thanks for the article. It comes up with a pretty good proof using the Weierstrass product of the Gamma function.

    I sincerely wonder how I could not find that one with two hours of searching.
     
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