Re: Series[] command

• To: mathgroup at smc.vnet.net
• Subject: [mg55944] Re: [mg55939] Series[] command
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Mon, 11 Apr 2005 03:14:53 -0400 (EDT)
• References: <200504110307.XAA06466@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```On 11 Apr 2005, at 12:07, Kris Preacher wrote:

> Hi all,
>
> I need to obtain the second-order Taylor series expansion of a*b
> around the
> points ma and mb. I thought Mathematica's Series[] command would do the
> trick, but no. The correct answer is:
>
> ma*mb + ma(b-mb) + mb(a-ma) + (a-ma)(b-mb)
>
> Mathematica gives:
>
> b(a-ma) + ma(b-mb) + ma*mb
>
>
> Thanks,
> Kris Preacher
> UNC
>
>

Simple: your two expressions are equal (both simplify to a*b) so they
are both equally correct. However, you can get your "expansion" in the
form you want as follows:

Normal[(ma+t*h)*(mb+t*k)+O[t]^3]/.t->1/.{h->(a-ma),k->b-mb}

(a-ma) (b-mb)+ma (b-mb)+(a-ma) mb+ma mb

Andrzej Kozlowski
Chiba, Japan
http://www.akikoz.net/andrzej/index.html
http://www.mimuw.edu.pl/~akoz/

```

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