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MathGroup Archive 1998

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Re: Multi-Variate Taylor Series Expansions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg14735] Re: [mg14718] Multi-Variate Taylor Series Expansions
  • From: me <me at talmanl1.mscd.edu>
  • Date: Wed, 11 Nov 1998 17:53:39 -0500
  • Sender: owner-wri-mathgroup at wolfram.com

One must use a trick to obtain multivariate Taylor polynomials.  Try

     Normal[Series[f[x + t h, y + t k], {t, 0, 3}]] /. t -> 1

--Lou Talman
  Department of Mathematical and Computer Sciences
  Campus Box 38
  Metropolitan State College of Denver
  PO Box 173362
  Denver CO 80217-3362

  http://clem.mscd.edu/~talmanl


> Date: Tue, 10 Nov 1998 01:21:08 -0500
> From: Tom Bell <tombell at stanford.edu>
To: mathgroup at smc.vnet.net
> To: mathgroup at smc.vnet.net
> Subject: [mg14735] [mg14718] Multi-Variate Taylor Series Expansions
> Mime-Version: 1.0
> 
> 
> Is there a function in Mathematica that will do multi-variate Taylor
> series
> 
> expansions?  For example, suppose I have
> 
> function = F(x + dx, t + dt)
> 
> then the expansion to second order about (x,t) should look something
> like
> 
> expansion = F(x,t) + dx D(F,x) + dt D(F,t) + (1/2) dx^2 D(F,{x,2}) +
> 
>     dx dt D(F,{x,t}) + (1/2) dt^2 D(F,{t,2}) + O(dx^3) + O(dt^3)
> 
> The situation gets a little more complicated: the function may look like
> 
> F(x + G(x + dx, t + dt), t + dt) and so on, so that the expansion should
> be
> 
> recursive.  After expanding F, the function should keep going back and
> expending G until no
> 
> further expansions can be done.
> 
> Please reply to tombell at stanford.edu, and thanks in advance for your
> help.
> 
> ---------------------------------------------------------------- 
> Thomas (Tom) Bell               
> Gravity Probe-B, H.E.P.L. tombell at stanford.edu
> Stanford University 136D Escondido Village          
> Stanford, CA
> 94305-4085 Stanford, CA 94305              650/725-6378 (o)
> 650/497-4230 (h)                650/725-8312 (fax)
> 



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