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Re: Series

  • To: mathgroup at smc.vnet.net
  • Subject: [mg42764] Re: Series
  • From: "Ersek, Ted R" <ErsekTR at navair.navy.mil>
  • Date: Fri, 25 Jul 2003 05:08:09 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Recall the recent thread about how to take a power series in two variables
and truncate it so the sum of exponents in each term does not exceed some
integer.  The programming needed to do this is a bit tricky for some users.
So I wrote a TrucatedSeries package and posted it at 
http://library.wolfram.com/infocenter/MathSource/4950/ 

Notice with my package we can get a TruncatedSeries about 
{x0,y0}={0,1} or {x0,y0,z0}={0,1,0} or even {x0,y0}={Infinity,0} as follows:

   TruncatedSeries[ Exp[x y]Log[y], {x,0}, {y,1}, 3 ]

   TruncatedSeries[ Exp[x y]Log[y]/(z-1), {x,0}, {y,1}, {z,0}, 3 ]

   TruncatedSeries[ ArcTan[x]/(y-1), {x,Infinity}, {y,0}, 3 ]

The solution posted at 
  http://forums.wolfram.com/mathgroup/archive/2003/Jul/msg00356.html
would only work when the series expansion is about {x0,y0} with (x0==y0).
That approach could be generalized for higher dimensions such as a series
about {x0,y0,z0} provided (x0==y0==z0).  My package doesn't have that
restriction.  However, my package will only do series in two or three
variables.

--------------------
Regards,
Ted Ersek

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