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 [