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Finding non trivial sum

  1. May 18, 2012 #1
    Hi. I tried to evaluate a definite integral of [itex]x^x[/itex] from [itex]0[/itex] to [itex]1[/itex] and I have reached following sum:

    [tex]\int_0^1 x^x = \sum_{n=1}^{\infty} \frac{(-n)^{1-n}}{n}[/tex]

    Is there an expression of this sum, for example in terms of Meijer G-function? I tried to find [itex]x^x[/itex] as G-function form to integrate it but unsuccessful.

    Thanks in advance.
     
  2. jcsd
  3. May 18, 2012 #2
    I'm not sure whether it's related to the G-function or not, but the sum itself is well-known, and is called the Sophomore's dream.
     
  4. May 18, 2012 #3
    Thanks, I didn't know it has a name; I will look for articles about it. Anyway I have reached the sum the same way as it is shown in your link.
     
  5. May 20, 2012 #4
  6. May 20, 2012 #5
    Hi, I've downloaded it even :). It was an answer to some of my questions. Thanks.
     
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