Are there closed form solutions to the harmonic series?

  • #1
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Are there closed form solutions to the harmonic series?
 

Answers and Replies

  • #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
 
  • #3
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yeah thats what i meant. thanks. also is most everything known about harmonic series? what is not known?

thanks
 

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