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Re: Hyperbolic function identity

• To: mathgroup at smc.vnet.net
• Subject: [mg50957] Re: Hyperbolic function identity
• From: "Peter Pein" <petsie at arcor.de>
• Date: Wed, 29 Sep 2004 03:15:35 -0400 (EDT)
• References: <cjasqk$ns0$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

"Carlos Felippa" <carlos at colorado.edu> schrieb im Newsbeitrag
news:cjasqk$ns0$1 at smc.vnet.net...
> 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 +
z^2/2])/Sqrt[2]]

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

 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 [