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MathGroup Archive 2007

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RE: Re: Showing that ArcSinh[2]/ArcCsch[2] is 3?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg73623] RE: [mg73550] Re: Showing that ArcSinh[2]/ArcCsch[2] is 3?
  • From: "Tony Harker" <a.harker at ucl.ac.uk>
  • Date: Fri, 23 Feb 2007 04:36:33 -0500 (EST)

Dear Oleksandr,

              That's interesting: but looking at what is produced by 
  ArcSinh[2]/ArcCsch[2] == 3 // FullSimplify
 makes me wonder just how Mathematica achieved this. In other words, what
does the message that Bob Hanlon so carefully suppressed mean? Similar
messages sometimes occur when checking the results of simple equations by
back-substituting, especially when the solutions contain surds, and appear
to show that Mathematica is diving off into real numbers to prove results
involving integers and powers of integers. 

   Tony


Dr A.H. Harker
Department of Physics and Astronomy
University College London
Gower Street
London
WC1E 6BT

 

]->-----Original Message-----
]->From: sashap [mailto:pavlyk at gmail.com] 
]->Sent: 21 February 2007 11:04
]->To: mathgroup at smc.vnet.net
]->Subject: [mg73550] Re: Showing that ArcSinh[2]/ArcCsch[2] is 3?
]->
]->Dear David,
]->
]->It is the case in the CAS and in the real life as well that 
]->proving left hand side equal to right hand side is easier 
]->than deriving what right hand side the left hand side equals to.
]->
]->I can not think of a direct way to use built-in 'knowledge' 
]->to reduce ArcSinh[2]/ArcCsch[2] to 3, but want to point out 
]->that proving it post-factum does not seem problematic:
]->
]->In[3]:=
]->ArcSinh[2]/ArcCsch[2]-3//FullSimplify
]->
]->Out[3]=
]->0
]->
]->Sincerely,
]->
]->Oleksandr Pavlyk
]->Special Functions Developer
]->Wolfram Research Inc
]->
]->On Feb 20, 5:24 am, "David W.Cantrell" 
]-><DWCantr... at sigmaxi.net> wrote:
]->> I hope I've just overlooked something very simple.
]->> I want to transform ArcSinh[2]/ArcCsch[2] to 3, using just 
]->"knowledge"
]->> already implemented in Mathematica. I tried FullSimplify 
]->first, and it 
]->> doesn't help. I tried several other things. For example,
]->>
]->> TrigToExp[ArcSinh[2]/ArcCsch[2]]  yields
]->>
]->> Log[2 + Sqrt[5]]/Log[1/2 + Sqrt[5]/2].
]->>
]->> But then how should we transform that to 3?
]->>
]->> David
]->
]->
]->
]->



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