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 > > Whaddup?? > > 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/

**References**:**Series[] command***From:*"Kris Preacher" <preacher@unc.edu>