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A mistake by Mathematica?

• To: mathgroup at smc.vnet.net
• Subject: [mg67796] A mistake by Mathematica?
• From: "LordBeotian" <pokipsy76 at ANTISPAMyahoo.it>
• Date: Sat, 8 Jul 2006 04:55:54 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

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. 

• Follow-Ups:
  • Re: A mistake by Mathematica?
    • From: Bruce Miller <brucem@wolfram.com>
  • Re: A mistake by Mathematica?
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>
  • Re: A mistake by Mathematica?
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>