Re: A mistake by Mathematica?
- To: mathgroup at smc.vnet.net
- Subject: [mg67817] Re: [mg67796] A mistake by Mathematica?
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Sun, 9 Jul 2006 04:50:33 -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
- References:
- A mistake by Mathematica?
- From: "LordBeotian" <pokipsy76@ANTISPAMyahoo.it>
- A mistake by Mathematica?