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MathGroup Archive 2002

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Re: Taylor Series Expansions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg32386] Re: [mg32372] Taylor Series Expansions
  • From: Hugh Walker <hwalker at gvtc.com>
  • Date: Thu, 17 Jan 2002 02:23:41 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Here is a variation on multi Taylor series I picked up from a Matggroup
resposne several years ago. Neat trick I think.
==========
Joe Helfand <jhelfand at wam.umd.edu> wrote:

taylorSeries[f_] := (Series[f/. Thread[{x,y,z}->eps {x,y,z}],
					{eps,0,n}]//Normal)/.eps->1
>Wow!
>
>    I have definitely come to the right place.  Thanks for all the
>responses.  Using the Map built in function solved my problem (it still
>took a bit, so you can imagine what I was dealing with).  Here is
>something else which I have wasted some time on not knowing as much
>about Mathematica as I should.  It has to do with multi-variable Taylor
>series expansion.  Mathematica has a built in Series function.  But when
>you use this for multi-variable functions, it doesn't do quite what I'd
>expect.  Let's say I have a function for two fariables, and I want to
>expand to 2nd order.  When I use Series, it expands each varible to
>second order, but includes the cross terms, which I want to belong to a
>4th order expansion.  For example:
>
>In[1172]:=
>Normal[Series[Exp[x y], {x, 0, 2}, {y, 0, 2}]]
>
>Out[1172]=
>\!\(1 + x\ y + \(x\^2\ y\^2\)\/2\)
>
>But what I really want is just 1 + x y, where if I go to fourth order,
>then I'll take the x^2 y^2 / 2.  I had to take some time to write some
>sloppy Taylor series expansion functions that did what I wanted.  Is
>there a way to get around this problem or do you have any suggestions?
>
>Thanks Again,
>Joe


    ==

Hugh Walker
Gnarly Oaks




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