I have the following output $\text{Li}_2\left(3-2 \sqrt{2}\right)-4 \text{Li}_2\left(-1+\sqrt{2}\right)$.

This turns out to be equivalent to $\displaystyle\log^2(1+\sqrt{2})-\frac{\pi^2}{4}$.

How can I get mathematica to simplify the first result to the second? I have other (more complicated) results like this that I need to simplify. FullSimplify and Simplify don't do anything, it just throws the same thing that I put in back at me...

FullSimplify[PolyLog[2, 3 - 2 Sqrt[2]] - 4 PolyLog[2, -1 + Sqrt[2]]]

  • $\begingroup$ @Mr.Wizard I think you have inputted it wrong. Li_2 means the function polylog_2 $\endgroup$ – user85798 Apr 16 '14 at 21:42
  • $\begingroup$ Okay. Please include Mathematica code also for your "equivalent" expression so that there is no more miscommunication. $\endgroup$ – Mr.Wizard Apr 16 '14 at 21:49
  • $\begingroup$ In version 7 FullSimplify[PolyLog[2, 3 - 2 Sqrt[2]] - 4 PolyLog[2, -1 + Sqrt[2]]] outputs -(Pi^2/4) + Log[1 + Sqrt[2]]^2, which is I believe what you want. Which version are you using? $\endgroup$ – Mr.Wizard Apr 16 '14 at 22:59
  • $\begingroup$ @Mr.Wizard I'm using version It doesn't work for me for some reason quickpic.info/z/1h.jpg $\endgroup$ – user85798 Apr 16 '14 at 23:15
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    $\begingroup$ FYI: I wasn't doubting your veracity, rather such things often need to be localized to which versions they affect to best address them. Thanks. $\endgroup$ – Mr.Wizard Apr 16 '14 at 23:51

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