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?