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Series expression for inverse hyperbolic function

  1. Nov 13, 2005 #1

    I'm trying to find a way to prove that
    \sum_{n=1}^{\infty} n e^{-n x} = \frac{1}{4}\sinh^{-2} \frac{x}{2}
    Any help greatly appreciated
  2. jcsd
  3. Nov 13, 2005 #2
    Do you know the sum of the geometric series ?
  4. Nov 13, 2005 #3
    I realised that it was the [itex]\sinh x[/itex] function and not the inverse function. And yes I used the geometric series to show the relation. Thanks anyways!
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