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MathGroup Archive 2004

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Re: Hyperbolic function identity

  • To: mathgroup at
  • Subject: [mg50957] Re: Hyperbolic function identity
  • From: "Peter Pein" <petsie at>
  • Date: Wed, 29 Sep 2004 03:15:35 -0400 (EDT)
  • References: <cjasqk$ns0$>
  • Sender: owner-wri-mathgroup at

"Carlos Felippa" <carlos at> schrieb im Newsbeitrag
news:cjasqk$ns0$1 at
> Why
>    FullSimplify[ArcCosh[1+z^2/2]-2*ArcSinh[z/2],z>0];
> does not evaluate to 0?

My guess is that

In[1]:= TrigToExp[ArcCosh[1 + z^2/2] - 2*ArcSinh[z/2]]
Out[1]= -2*Log[z/2 + Sqrt[1 + z^2/4]] + Log[1 + z^2/2 + (Sqrt[z^2]*Sqrt[2 +

"looks too complicated" to Mathematica's ComplexityFunction to follow this

 The strange thing is that, in version 4 at least,
FullSimplify[TrigToExp[ArcCosh[1 + z^2/2] - 2*ArcSinh[z/2]], z>0]
leads to the desired result, but appending TrigToExp to the list of the
TransformationFunctions does not.
Peter Pein, Berlin
to write to me, start the subject with [

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