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Euler constants

  1. Jul 21, 2009 #1
    is the following sequence finite

    [tex] \sum_{n=1}^{\infty} \frac{log^{u-1} (n)}{n} - u^{-1}log^{u}(n) [/tex]

    if u=1 then we have simply the Euler-Mascheroni constant but what happens in other cases or other values for 'u'
     
  2. jcsd
  3. Jul 21, 2009 #2

    CRGreathouse

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    I'm going to go out on a limb and guess that when you write
    [tex] \sum_{n=1}^{\infty} \frac{log^{u-1} (n)}{n} - u^{-1}log^{u}(n) [/tex]
    you mean something like
    [tex]\lim_{x\to\infty}-(\log x)^u+\sum_{n=1}^x\frac{(\log n)^{u-1}}{n}[/tex]
    but you may mean something else entirely.
     
  4. Jul 22, 2009 #3
    no but thanks by the answer i meant

    [tex] \sum_{n=1}^{\infty} \frac{log^{u-1}(n)}{n} - \int_{1}^{\infty}\frac{log^{u-1}(x)}{x} [/tex]

    in case u=1 we have the Euler Mascheroni constant but how about for other values ??
     
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