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Re: A mistake by Mathematica?

• To: mathgroup at smc.vnet.net
• Subject: [mg67841] Re: A mistake by Mathematica?
• From: "LordBeotian" <pokipsy76 at ANTISPAMyahoo.it>
• Date: Mon, 10 Jul 2006 06:37:50 -0400 (EDT)
• References: <200607080855.EAA20385@smc.vnet.net> <e8qg0g$o28$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

"Andrzej Kozlowski" <akoz at mimuw.edu.pl> ha scritto

> When you do not tell us what exaclty you did we have no way of  
> knowing if it is Mathematica or your who made the mistake. In any  
> case, I get the same answer using both approaches:
> 
> 
> f[x_, e_] := 2*((3*e^4)/2 + e^5 + e^6 - (e^2*x^2)/2 +
>      (1/3)*e^2*x^3 + x^4/24 + (e^2*x^4)/24 -
>      (1/15)*e^2*x^5 - x^6/720 - (e^2*x^6)/720)^(1/2)
> 
> 
> 
> Normal[f[x,0]+O[x]^5]
> 
> 
> x^2/Sqrt[6] - x^4/(60*Sqrt[6])
> 
> 
> 
> Apart[Limit[Normal[f[t*x, t*e] + O[t]^5] /. t -> 1,
>    e -> 0,Assumptions->x>=0]]

Instead of that I computed this:

Limit[Normal[f[x, e] + O[x]^4], e -> 0]
The result was

((x^2 (((-3) + 2 x)))/(3 Sqrt[6]))

I think the problem could be due to the fact that f is not(?) C^3 in (0,0).
Thank you for your help.

• References:
  • A mistake by Mathematica?
    • From: "LordBeotian" <pokipsy76@ANTISPAMyahoo.it>