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MathGroup Archive 1998

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Multi-Variate Taylor Series Expansions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg14718] Multi-Variate Taylor Series Expansions
  • From: Tom Bell <tombell at stanford.edu>
  • Date: Tue, 10 Nov 1998 01:21:08 -0500
  • Sender: owner-wri-mathgroup at wolfram.com

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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