       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
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```

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