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MathGroup Archive 2002

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Re: Taylor Series Expansions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg32379] Re: [mg32372] Taylor Series Expansions
  • From: BobHanlon at aol.com
  • Date: Thu, 17 Jan 2002 02:23:32 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

In a message dated 1/16/02 5:45:03 AM, jhelfand at wam.umd.edu writes:

>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.

k=6;
Normal[Series[Exp[x y],{x,0,k},{y,0,k}]]

(x^6*y^6)/720 + (x^5*y^5)/120 + (x^4*y^4)/24 + (x^3*y^3)/6 + 
  (x^2*y^2)/2 + x*y + 1

%/. ((a_*x^m_*y^n_) /; m+n>k):>0

(x^3*y^3)/6 + (x^2*y^2)/2 + x*y + 1

%%/. ((a_*x^m_*y^n_) /; m+n>2):>0

x*y + 1


Bob Hanlon
Chantilly, VA  USA


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