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

[AxiomOfChoice]

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

$$\cosh^{-1}(\sqrt{2})$$

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

Thanks!

UPDATE: Looks like Maple 11 refuses to evaluate $$\cosh^{-1}(\sqrt{2})$$ too. What is going on here?!

 

[mgb_phys]

Don't know, have you tried ln(x+root(x^2-1)) instead?

 

[Gokul43201]

I have no trouble with this in Mathematica 6. What is your error message?

Here's a screenshot:

http://img522.imageshack.us/img522/3521/picture23nm3.png

 

[CRGreathouse]

http://www.research.att.com/~njas/sequences/A091648

 

[Phrak]

It could be a problem if you have replaced this $\sqrt{2}$ with this $2^{1/2}$.

 

[Gokul43201]

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.

 

[CRGreathouse]

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.

 

[uart]

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.