Why is Mathematica giving me fits when I try to evaluate ArcCosh[Sqrt[2]]?

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Discussion Overview

The discussion revolves around the difficulties participants are experiencing when trying to evaluate the inverse hyperbolic cosine function, specifically ArcCosh[Sqrt[2]], in Mathematica and Maple software. The scope includes technical explanations and potential troubleshooting methods related to symbolic computation.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses confusion over Mathematica's inability to evaluate \cosh^{-1}(\sqrt{2}) and questions whether it is undefined.
  • Another participant suggests using the natural logarithm formula ln(x + sqrt(x^2 - 1)) as an alternative approach.
  • A different participant reports no issues with Mathematica 6 and asks for the specific error message encountered by the original poster.
  • One participant speculates that the issue may arise from using different representations of \sqrt{2}, such as 2^{1/2}.
  • There are suggestions for obtaining a decimal approximation using the Round function in Mathematica.
  • A participant clarifies that Maple will not return a decimal approximation unless explicitly instructed to do so, indicating a difference in functionality between versions of Maple.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the cause of the evaluation issue, with multiple competing views and suggestions presented regarding the use of different software and methods.

Contextual Notes

Limitations include potential misunderstandings of software functionality, differences in software versions, and the representation of mathematical expressions that may affect evaluation.

AxiomOfChoice
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For some reason, Mathematica will not comply when I try to determine

[tex] \cosh^{-1}(\sqrt{2})[/tex]

Why is this the case? Is [tex]\cosh^{-1}(x)[/tex] undefined there or something? If so, why? I don't really see it...

Thanks!

UPDATE: Looks like Maple 11 refuses to evaluate [tex]\cosh^{-1}(\sqrt{2})[/tex] too. What is going on here?!
 
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Don't know, have you tried ln(x+root(x^2-1)) instead?
 
http://www.research.att.com/~njas/sequences/A091648
 
Last edited by a moderator:
It could be a problem if you have replaced this [itex]\sqrt{2}[/itex] with this [itex]2^{1/2}[/itex].
 
CRGreathouse said:
http://www.research.att.com/~njas/sequences/A091648
If the OP is looking for a decimal approximation, then something along the lines of Round[ArcCosh[Sqrt[2]],0.0001] should work just as well on Mathematica.
 
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Gokul43201 said:
If the OP is looking for a decimal approximation, then something along the lines of Round[ArcCosh[Sqrt[2]],0.0001] should work just as well on Mathematica.

I thought the additional information there (inflection point, etc) might be relevant the the unstated underlying problem.
 
UPDATE: Looks like Maple 11 refuses to evaluate "cosh^{-1}(\\sqrt{2})" too. What is going on here

Hi AxiomOfChoice, what exactly do you mean by evaluate in this case? Maple will try to symbolically simply an expression, it won't return a decimal approximation unless you tell it to (typically using the "evalf" function.

I've got Maple 7 and "evalf(arccosh(sqrt(2)));" returns 0.8813735866.
 
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