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Re: A mistake by Mathematica?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg67848] Re: [mg67796] A mistake by Mathematica?
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Mon, 10 Jul 2006 06:38:13 -0400 (EDT)
  • References: <200607080855.EAA20385@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

On 8 Jul 2006, at 09:55, LordBeotian wrote:

> I have defined a function f[x,e] that is continuous in both variables.
> Then I ask Mathematica to do this 2 operations:
> 1) produce the series of f[x,0] up to 4th order
> 2) produce the series of f[x,e] and then compute the limit of the  
> coefficient
> for e->0
> I think the results of both operation should be the same. Instead  
> just the
> first coefficient is the same, the coefficient of x^3 different and  
> higher
> order coefficient become infinity in the second computation!
>
> Is it a problem with the program itself or am I missing something?
> Thank you.
>
> PS:
> I don't think if it is relevant but the function is the following:
> \!\(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)\)^\((1/2)\)\)
> it is continuous but there is a square root.
>

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]]


x^2/Sqrt[6] - x^4/(60*Sqrt[6])


I suspect you incorrectly obtianed the series for f[x,e].

Andrzej Kozlowski


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