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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