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MathGroup Archive 2003

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Re: series expansions in two variables problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg39528] Re: series expansions in two variables problem
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Fri, 21 Feb 2003 04:08:23 -0500 (EST)
  • Organization: The University of Western Australia
  • References: <b329vc$b2q$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

In article <b329vc$b2q$1 at smc.vnet.net>, mc799 at ic.ac.uk (Martin) wrote:

> I'm expanding an expression in two variables (sigma and epsilon, say),
> but am having trouble persuading Mathematica to chuck away terms of
> form epsilon*sigma.
> 
> ie I'm getting
> 
> A + B*sigma + C*epsilon + D*sigma*epsilon + O(sigma^2) + O(epsilon^2)
> 
> and I'd like very much to lose the D terms.

The trick (which you will find in the MathGroup archive) is not to 
expand in a series in both sigma and epsilon but to instead rescale the 
variables by a parameter, say q, and then expand into a series in q, 
truncating, and then setting q ->1. Here is a routine that does this:

 Truncate[x_, p_List, n_] := 
   Module[{q}, Normal[(x /. Thread[p -> q p]) + O[q]^n] /. q -> 1]

Here x is the expression, p is the List of variables and n is the 
truncation order.

 Truncate[a+ b sigma + c epsilon + d sigma epsilon, {sigma,epsilon},2]

Cheers,
Paul

-- 
Paul Abbott                                   Phone: +61 8 9380 2734
School of Physics, M013                         Fax: +61 8 9380 1014
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Crawley WA 6009                      mailto:paul at physics.uwa.edu.au 
AUSTRALIA                            http://physics.uwa.edu.au/~paul



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