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Are there closed form solutions to the harmonic series?

  1. Mar 22, 2005 #1
    Are there closed form solutions to the harmonic series?
     
  2. jcsd
  3. Mar 22, 2005 #2

    HallsofIvy

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    Sure. The sum [tex]\Sigma_{k=1}^{n}\frac{1}{k}= \gamma+ \Psi_0(n+1)[/tex] where [tex]\gamma[/tex] is the "Euler-Mascheroni" constant and [tex]\Psi_0[/tex] is the digamma function. Or did you mean something else by "closed form"?

    See
    http://mathworld.wolfram.com/HarmonicSeries.html
     
  4. Mar 22, 2005 #3
    yeah thats what i meant. thanks. also is most everything known about harmonic series? what is not known?

    thanks
     
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