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MathGroup Archive 2004

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Re: Hyperbolic function identity

  • To: mathgroup at smc.vnet.net
  • Subject: [mg50944] Re: [mg50932] Hyperbolic function identity
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Wed, 29 Sep 2004 03:15:06 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

This also works


FullSimplify[ComplexExpand[ArcCosh[1 + z^2/2] - 2*ArcSinh[z/2]], z > 0]

0

However, it essentially amounts to the same thing as using TrigToExp.

Andrzej

On 28 Sep 2004, at 15:07, Andrzej Kozlowski wrote:

>
> On 28 Sep 2004, at 13:58, Carlos Felippa wrote:
>
>> *This message was transferred with a trial version of CommuniGate(tm) 
>> Pro*
>> Why
>>
>>    FullSimplify[ArcCosh[1+z^2/2]-2*ArcSinh[z/2],z>0];
>>
>> does not evaluate to 0?
>>
>>
>
> This works.
>
>
> FullSimplify[TrigToExp[ArcCosh[1 + z^2/2] - 2*ArcSinh[z/2]], z > 0]
>
> 0
>
> I think TrigToExp is already among the functions that  FullSimplify 
> uses and indeed this does not help:
>
>
> FullSimplify[ArcCosh[1 + z^2/2] - 2*ArcSinh[z/2], z > 0,
>   TransformationFunctions -> {Automatic, TrigToExp}]
>
> ArcCosh[z^2/2 + 1] - 2*ArcSinh[z/2]
>
> However, this again works:
>
>
> Simplify[ArcCosh[1+z^2/2]-2*ArcSinh[z/
>         2],z>0,TransformationFunctions->{Automatic,
>     FullSimplify[TrigToExp[#],z>0]&}]
>
> 0
>
>
> Andrzej Kozlowski
> Chiba, Japan
> http://www.akikoz.net/~andrzej/
> http://www.mimuw.edu.pl/~akoz/
>


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