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MathGroup Archive 2004

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Re: Remove the higher order terms in series expansion

  • To: mathgroup at smc.vnet.net
  • Subject: [mg52830] Re: Remove the higher order terms in series expansion
  • From: David Bailey <dave at Remove_Thisdbailey.co.uk>
  • Date: Tue, 14 Dec 2004 05:59:26 -0500 (EST)
  • References: <cpjpt7$nob$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

highorder wrote:
> I guess this should be simple and hiding somewhere in the manual. Is
> there a quick way to remove the high order terms after using
> Series[f,{x,x0,n}] command? The problem comes from the output is
> actually given by:
> 
> expansion term + O(x^3);
> 
> the O(x^3) should be removed. I will keep trying but wondering if
> anyone has a quick answer.
> 
> Thanks.
> 

Hi,

The short answer is very quick indeed - just use //Normal - that will 
remove the O[x]^3 term (note: not O[x^3]).

If you want to understand this a little more, look at a series expansion 
using //FullForm  (if in doubt, FullForm is always a good bet) - you 
will see that there is a special SeriesData structure used - that is why 
you can't simply remove the O[x]^3 term. Because Mathematica 'remembers' 
that these things are series, it can do sensible arithmetic on them - 
for example, you can add or multiply series together keeping track of 
the number of valid terms in the result.

David Bailey
dbaileyconsultancy.co.uk


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